Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 27 Feb 2010
Posts: 70
Location: Denver

For which of the following functions is f(a + b) = f(a) + f(b) for all
[#permalink]
Show Tags
23 Apr 2010, 15:24
Question Stats:
76% (01:42) correct 24% (01:25) wrong based on 1382 sessions
HideShow timer Statistics
For which of the following functions is f(a + b) = f(a) + f(b) for all positive numbers a and b? A. \(f(x)=x^2\) B. \(f(x)= x+1\) C. \(f(x) = \sqrt{x}\) D. \(f(x)=\frac{2}{x}\) E. \(f(x) = 3x\)
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 65763

Re: function F(x)
[#permalink]
Show Tags
15 Jan 2012, 15:06
Responding to a PM. For which of the following functions is f(a+b)= f(a)+f(b) for all positive numbers a and b?A. \(f(x)=x^2\) B. \(f(x)= x+1\) C. \(f(x) = \sqrt{x}\) D. \(f(x)=\frac{2}{x}\) E. \(f(x) = 3x\) A. \(f(a+b)=(a+b)^2=a^2+2ab+b^2\neq{f(a)+f(b)}=a^2+b^2\) B. \(f(a+b)=(a+b)+1\neq{f(a)+f(b)}=a+1+b+1\) C. \(f(a+b)=\sqrt{a+b}\neq{f(a)+f(b)}=\sqrt{a}+\sqrt{b}\). D. \(f(a+b)=\frac{2}{a+b}\neq{f(a)+f(b)}=\frac{2}{a}+\frac{2}{b}\). E. \(f(a+b)=3(a+b)=3a3b=f(a)+f(b)=3a3b\). Correct. Answer: E. OR, as f(a+b)= f(a)+f(b) must be true for all positive numbers a and b, then you can randomly pick particular values of a and b and check for them: For example: \(a=2\) and \(b=3\) A. \(f(a + b) = f(5) = 5^2 = 25\neq{f(a) + f(b) = f(2) + f(3) = 2^2 + 3^2 = 13}\) B. \(f(a + b) = f(5) = 5 + 1 = 6\neq{f(a) + f(b) = f(2) + f(3) = (2 + 1) + (3 + 1) = 7}\) C. \(f(a + b)=f(5)=\sqrt{5}\neq{f(a) + f(b)=f(2)+f(3)=\sqrt{2}+\sqrt{3}}\) D. \(f(a + b)=f(5)=\frac{2}{5}\neq{f(a)+f(b)=f(2)+f(3)=\frac{2}{2}+\frac{2}{3}=\frac{5}{3}}\) E. \(f(a + b)=f(5)=3*(5) =15=f(a)+f(b)=f(2)+f(3)=3*(2)3*(3)=15\). Correct. It might happen that for some choices of a and b other options may be "correct" as well. If this happens just pick some other numbers and check again these "correct" options only. Similar questions to practice: function85751.htmlfunctionsproblemneedhelp93184.htmlletthefunctiongabfafb143311.htmlHope it helps.
_________________



GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4985
Location: Canada

Re: For which of the following functions is f(a+b)=f(b)+f(a)
[#permalink]
Show Tags
06 Feb 2018, 14:50
enigma123 wrote: For which of the following functions is f(a+b)=f(b)+f(a) for all positive numbers a and b?
A. f(x)=x^2 B. f(x)=x+1 C. f(x)=√x D. f(x)=2/x E. f(x)=3x
One approach is to plug in numbers. Let's let a = 1 and b = 1So, the question becomes, "Which of the following functions are such that f(1+1) = f(1) + f(1)?" In other words, for which function does f(2) = f(1) + f(1)?A) If f(x)=x², does f( 2) = f( 1) + f( 1)? Plug in to get: 2² = 1² + 1²? (No, doesn't work) So, it is not the case that f( 2) = f( 1) + f( 1), when f(x)=x² B) If f(x)=x+1, does f( 2) = f( 1) + f( 1)? Plug in to get: 2+1 = 1+1 + 1+1? (No, doesn't work) So, it is not the case that f( 2) = f( 1) + f( 1) . . . A, B, C and D do not work. So, at this point, we can conclude that E must be the correct answer. Let's check E anyway (for "fun") E) If f(x)=3x, does f( 2) = f( 1) + f( 1)? Plugging in 2 and 1 we get: (3)( 2) = (3)( 1) + (3)( 1) Yes, it works The correct answer is E Cheers, Brent
_________________
If you enjoy my solutions, you'll love my GMAT prep course.




Manager
Joined: 12 Jul 2011
Posts: 76
Concentration: Operations, Strategy
WE: Engineering (Telecommunications)

Re: function F(x)
[#permalink]
Show Tags
12 Dec 2011, 06:47
Question asks you to check which of the provided options satisfy the equality "f(a+b) = f(a) + f(b)" Answer is E, if you apply f(x) = 3x to f(a+b) then f(a+b) = 3(a+b) = 3a 3b f(a) = 3a f(b) = 3b f(a) + f(b) = 3a 3b = f(a+b) Hope I am clear.




Math Expert
Joined: 02 Sep 2009
Posts: 65763

For which of the following functions is f(a + b) = f(a) + f(b) for all
[#permalink]
Show Tags
24 Apr 2010, 06:02
For which of the following functions is f(a+b)= f(a)+f(b) for all positive numbers a and b?A. \(f(x)=x^2\) B. \(f(x)= x+1\) C. \(f(x) = \sqrt{x}\) D. \(f(x)=\frac{2}{x}\) E. \(f(x) = 3x\) A. \(f(a+b)=(a+b)^2=a^2+2ab+b^2\neq{f(a)+f(b)}=a^2+b^2\) B. \(f(a+b)=(a+b)+1\neq{f(a)+f(b)}=a+1+b+1\) C. \(f(a+b)=\sqrt{a+b}\neq{f(a)+f(b)}=\sqrt{a}+\sqrt{b}\). D. \(f(a+b)=\frac{2}{a+b}\neq{f(a)+f(b)}=\frac{2}{a}+\frac{2}{b}\). E. \(f(a+b)=3(a+b)=3a3b=f(a)+f(b)=3a3b\). Correct. Answer: E.OR, as f(a+b)= f(a)+f(b) must be true for all positive numbers a and b, then you can randomly pick particular values of a and b and check for them: For example: \(a=2\) and \(b=3\) A. \(f(a + b) = f(5) = 5^2 = 25\neq{f(a) + f(b) = f(2) + f(3) = 2^2 + 3^2 = 13}\) B. \(f(a + b) = f(5) = 5 + 1 = 6\neq{f(a) + f(b) = f(2) + f(3) = (2 + 1) + (3 + 1) = 7}\) C. \(f(a + b)=f(5)=\sqrt{5}\neq{f(a) + f(b)=f(2)+f(3)=\sqrt{2}+\sqrt{3}}\) D. \(f(a + b)=f(5)=\frac{2}{5}\neq{f(a)+f(b)=f(2)+f(3)=\frac{2}{2}+\frac{2}{3}=\frac{5}{3}}\) E. \(f(a + b)=f(5)=3*(5) =15=f(a)+f(b)=f(2)+f(3)=3*(2)3*(3)=15\). Correct. It might happen that for some choices of a and b other options may be "correct" as well. If this happens just pick some other numbers and check again these "correct" options only. Similar questions: http://gmatclub.com/forum/forwhichof ... 24491.htmlhttp://gmatclub.com/forum/forwhichof ... 85751.htmlhttp://gmatclub.com/forum/letthefunct ... 43311.htmlHope it helps.
_________________



Manager
Joined: 27 Feb 2010
Posts: 70
Location: Denver

Re: For which of the following functions is f(a + b) = f(a) + f(b) for all
[#permalink]
Show Tags
24 Apr 2010, 09:23
Thank you Bunuel. This is really a good explaination. I did some samples based on your explaination and i am confident that I can handle these kind or problems.



Manager
Joined: 05 Mar 2010
Posts: 138

Re: For which of the following functions is f(a + b) = f(a) + f(b) for all
[#permalink]
Show Tags
24 Apr 2010, 09:36
Bunuel wrote: hardnstrong wrote: yes can anyone explain how to proceed with function problems .....this is one of my weakest area For which of the following functions is f(a+b)= f(a)+f(b) for all positive numbers a and b? A. \(f(x)=x^2\) B. \(f(x)= x+1\) C. \(f(x) = \sqrt{x}\) D. \(f(x)=\frac{2}{x}\) E. \(f(x) = 3x\) A. \(f(a+b)=(a+b)^2=a^2+2ab+b^2\neq{f(a)+f(b)}=a^2+b^2\) B. \(f(a+b)=(a+b)+1\neq{f(a)+f(b)}=a+1+b+1\) C. \(f(a+b)=\sqrt{a+b}\neq{f(a)+f(b)}=\sqrt{a}+\sqrt{b}\). D. \(f(a+b)=\frac{2}{a+b}\neq{f(a)+f(b)}=\frac{2}{a}+\frac{2}{b}\). E. \(f(a+b)=3(a+b)=3a3b=f(a)+f(b)=3a3b\). Correct. Answer: E. OR, as f(a+b)= f(a)+f(b) must be true for all positive numbers a and b, then you can randomly pick particular values of a and b and check for them: For example: \(a=2\) and \(b=3\) A. \(f(a + b) = f(5) = 5^2 = 25\neq{f(a) + f(b) = f(2) + f(3) = 2^2 + 3^2 = 13}\) B. \(f(a + b) = f(5) = 5 + 1 = 6\neq{f(a) + f(b) = f(2) + f(3) = (2 + 1) + (3 + 1) = 7}\) C. \(f(a + b)=f(5)=\sqrt{5}\neq{f(a) + f(b)=f(2)+f(3)=\sqrt{2}+\sqrt{3}}\) D. \(f(a + b)=f(5)=\frac{2}{5}\neq{f(a)+f(b)=f(2)+f(3)=\frac{2}{2}+\frac{2}{3}=\frac{5}{3}}\) E. \(f(a + b)=f(5)=3*(5) =15=f(a)+f(b)=f(2)+f(3)=3*(2)3*(3)=15\). Correct. It might happen that for some choices of a and b other options may be "correct" as well. If this happens just pick some other numbers and check again these "correct" options only. Hope it helps. Thanks bunuel You have solved my problem here. i think i can handle these questions now +1
_________________



Intern
Joined: 21 Apr 2010
Posts: 7

Re: For which of the following functions is f(a + b) = f(a) + f(b) for all
[#permalink]
Show Tags
24 Apr 2010, 14:51
Bunuel wrote: hardnstrong wrote: yes can anyone explain how to proceed with function problems .....this is one of my weakest area For which of the following functions is f(a+b)= f(a)+f(b) for all positive numbers a and b? A. \(f(x)=x^2\) B. \(f(x)= x+1\) C. \(f(x) = \sqrt{x}\) D. \(f(x)=\frac{2}{x}\) E. \(f(x) = 3x\) A. \(f(a+b)=(a+b)^2=a^2+2ab+b^2\neq{f(a)+f(b)}=a^2+b^2\) B. \(f(a+b)=(a+b)+1\neq{f(a)+f(b)}=a+1+b+1\) C. \(f(a+b)=\sqrt{a+b}\neq{f(a)+f(b)}=\sqrt{a}+\sqrt{b}\). D. \(f(a+b)=\frac{2}{a+b}\neq{f(a)+f(b)}=\frac{2}{a}+\frac{2}{b}\). E. \(f(a+b)=3(a+b)=3a3b=f(a)+f(b)=3a3b\). Correct. Answer: E. OR, as f(a+b)= f(a)+f(b) must be true for all positive numbers a and b, then you can randomly pick particular values of a and b and check for them: For example: \(a=2\) and \(b=3\) A. \(f(a + b) = f(5) = 5^2 = 25\neq{f(a) + f(b) = f(2) + f(3) = 2^2 + 3^2 = 13}\) B. \(f(a + b) = f(5) = 5 + 1 = 6\neq{f(a) + f(b) = f(2) + f(3) = (2 + 1) + (3 + 1) = 7}\) C. \(f(a + b)=f(5)=\sqrt{5}\neq{f(a) + f(b)=f(2)+f(3)=\sqrt{2}+\sqrt{3}}\) D. \(f(a + b)=f(5)=\frac{2}{5}\neq{f(a)+f(b)=f(2)+f(3)=\frac{2}{2}+\frac{2}{3}=\frac{5}{3}}\) E. \(f(a + b)=f(5)=3*(5) =15=f(a)+f(b)=f(2)+f(3)=3*(2)3*(3)=15\). Correct. It might happen that for some choices of a and b other options may be "correct" as well. If this happens just pick some other numbers and check again these "correct" options only. Hope it helps. thanks a ton for the explanation. There are not many problems on functions in samples and I am glad now i know how to go about for questions ike this.



Manager
Joined: 03 May 2010
Posts: 72
WE 1: 2 yrs  Oilfield Service

Re: For which of the following functions is f(a + b) = f(a) + f(b) for all
[#permalink]
Show Tags
15 Jun 2010, 05:12
For these kind of questions where you have to test each choice, ALWAYS start with E.
E. f(x) = 3x f(a+b) = 3(a+b) = 3a 3b f(a) = 3a ; f(b) = 3b f(a) + f(b)= 3a 3b = f(a+b)
On test day  stop.
Remember, just substitute for x with whatever is in the brackets in f ( )



SVP
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1808
Concentration: General Management, Nonprofit

Re: For which of the following functions is f(a + b) = f(a) + f(b) for all
[#permalink]
Show Tags
15 Jun 2010, 05:22
I agree with AbhayPrasanna.
If you want an explanation of why it doesn't work for the other functions, look at the type of each function.
\(x^2\) is a quadratic function, so \(f(a+b) = (a+b)^2\) and \(f(a) + f(b) = a^2 + b^2\)  Wrong
\(x+1\) has a constant variable in it, though its linear. So \(f(a+b) = a+b+1\) and \(f(a) + f(b) = (a+1)+(b+1) = a+b+2\)  Wrong
\(\sqrt{x}\) is a root function. \(f(a+b) = \sqrt{a+b}\) and \(f(a)+f(b) = \sqrt{a}+\sqrt{b}\)  Wrong
\(2/x\) is a fraction type function. So \(f(a+b) = 2/(a+b)\) and \(f(a)+f(b) = 2/a + 2/b = 2(a+b)/ab\)  Wrong
\(3x\) is a linear function without constants. So this must be the answer. But to check:
\(f(a+b) = 3*(a+b)\) and \(f(a) + f(b) = 3*a + (3*b) = 3* (a+b)\)  Right
This kind of elimination is not necessary on the exam. However, it's good to know why the other options don't work.



Manager
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 89
Concentration: Finance, General Management

Re: For which of the following functions is f(a + b) = f(a) + f(b) for all
[#permalink]
Show Tags
03 Jan 2011, 19:52
Bunuel wrote: hardnstrong wrote: yes can anyone explain how to proceed with function problems .....this is one of my weakest area For which of the following functions is f(a+b)= f(a)+f(b) for all positive numbers a and b? A. \(f(x)=x^2\) B. \(f(x)= x+1\) C. \(f(x) = \sqrt{x}\) D. \(f(x)=\frac{2}{x}\) E. \(f(x) = 3x\) A. \(f(a+b)=(a+b)^2=a^2+2ab+b^2\neq{f(a)+f(b)}=a^2+b^2\) B. \(f(a+b)=(a+b)+1\neq{f(a)+f(b)}=a+1+b+1\) C. \(f(a+b)=\sqrt{a+b}\neq{f(a)+f(b)}=\sqrt{a}+\sqrt{b}\). D. \(f(a+b)=\frac{2}{a+b}\neq{f(a)+f(b)}=\frac{2}{a}+\frac{2}{b}\). E. \(f(a+b)=3(a+b)=3a3b=f(a)+f(b)=3a3b\). Correct. Answer: E. OR, as f(a+b)= f(a)+f(b) must be true for all positive numbers a and b, then you can randomly pick particular values of a and b and check for them: For example: \(a=2\) and \(b=3\) A. \(f(a + b) = f(5) = 5^2 = 25\neq{f(a) + f(b) = f(2) + f(3) = 2^2 + 3^2 = 13}\) B. \(f(a + b) = f(5) = 5 + 1 = 6\neq{f(a) + f(b) = f(2) + f(3) = (2 + 1) + (3 + 1) = 7}\) C. \(f(a + b)=f(5)=\sqrt{5}\neq{f(a) + f(b)=f(2)+f(3)=\sqrt{2}+\sqrt{3}}\) D. \(f(a + b)=f(5)=\frac{2}{5}\neq{f(a)+f(b)=f(2)+f(3)=\frac{2}{2}+\frac{2}{3}=\frac{5}{3}}\) E. \(f(a + b)=f(5)=3*(5) =15=f(a)+f(b)=f(2)+f(3)=3*(2)3*(3)=15\). Correct. It might happen that for some choices of a and b other options may be "correct" as well. If this happens just pick some other numbers and check again these "correct" options only. Hope it helps. Thanks for really fleshing out the algebra on this problem Bunuel. The problems seem fairly easy once you understand how to work functions properly.



Manager
Joined: 09 Nov 2011
Posts: 102

Re: function F(x)
[#permalink]
Show Tags
22 Dec 2011, 09:08
f(a+b) has to be equal to f(a) + f(b)
A. f(x)=x^2 B. f(x)=x+1 C. f(x)=√x D. f(x)=2/x E. f(x)=3x
A) f(x) = x^2 f(a) = a^2; f(b)=b^2 f(a+b) = (a+b)^2 = a^2+b^2 +2ab f(a) +f(b) = a^2 + b^2 <> f(a+b)
so on and so forth...each option will lead to the same result except for E
Moreover, just by observing it can be found out the square roots, sqaures and x in the denominator will not be correct answers hence just try with E and you can find out..



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10780
Location: Pune, India

Re: For which of the following functions is f(a+b)=f(b)+f(a)
[#permalink]
Show Tags
16 Jan 2012, 01:00
enigma123 wrote: For which of the following functions is f(a+b)=f(b)+f(a) for all positive numbers a and b? A. f(x)=x^2 B. f(x)=x+1 C. f(x)=√x D. f(x)=2/x E. f(x)=3x
Can someone please tell me how to solve this? As OA is not provided I started by substituing the value of f(x) in the answer choice but got stuck. Can someone please help? You can save time by using an intuitive method. Look for the expression that satisfies the distributive property i.e. x * (y + z) = (x * y) + (x * z) When you put (a+b), it should give you individual functions in a and b which means that you will get two separate, comparable terms in a and b. Squares, roots, addition and division by the variable does not satisfy the distributive property. Multiplication does. So check for option (E) first. One rule of thumb  in such questions, try the options which have multiplication/addition first. These two operators have various properties which make such relations possible.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Director
Joined: 22 Mar 2011
Posts: 576
WE: Science (Education)

Re: Function Problem
[#permalink]
Show Tags
07 Sep 2012, 22:17
BigUp wrote: Hello GmatClub,
Could someone please help me to understand this gmatprep question? Thanks!
For which of the following functions is f(a+b) = f(a)+f(b) for all positive numbers a and b?
f(x)=x^2 f(x)=x+1 f(x)=sqrt(x) f(x)=2/x f(x)=3x First, a remark: \(a\) and \(b\) are considered positive because the function in C, the square root is not defined for negative numbers and the function in D is not defined for \(x=0\) (\(x\) being in the denominator). The other functions are defined for any real number. For each function, we translate the given equality and check whether is holds for any positive \(a\) and \(b\). If the equality holds for any \(a\) and \(b\), we should get an identity, which means the same expression on both sides of the equal sign. For \(f(a+b)\) we take the expression of any of the given functions and replace \(x\) by \((a+b)\). (A) \((a+b)^2=a^2+b^2\) or \(a^2+2ab+b^2=a^2+b^2\). Necessarily \(ab=0\), which cannot hold, \(a\) an \(b\) being positive. NO (B) \(a+b+1=a+1+b+1\) gives \(1=2\), impossible. NO (C) \(\sqrt{a+b}=\sqrt{a}+\sqrt{b}\) NO (check for example \(a=b=1\)) (D) \(\frac{2}{a+b}=\frac{2}{b}+\frac{2}{b}\) NO (again, check for \(a=b=1\)) (E) \(3(a+b)=3a+(3b)\) or \(3a3b=3a3b\) YES!!! Answer E.
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Senior Manager
Joined: 13 Aug 2012
Posts: 385
Concentration: Marketing, Finance
GPA: 3.23

For which of the following functions is f(a+b)=f(b)+f(a)
[#permalink]
Show Tags
20 Dec 2012, 22:06
Best to answer this with tinywinie numbers such as a=1, b=1 and a+b=1...
A. (1) + (1) = 4 OUT! B. (1+1) + (1+1) = 3 OUT! C. 1 + 1 = \(\sqrt{2}\) OUT! D. 2/1 + 2/1 = 2/2 OUT! E. 3(1) 3(1) = 3(2) BINGO!
Answer: E



Intern
Joined: 22 May 2013
Posts: 43
Concentration: General Management, Technology
GPA: 3.9
WE: Information Technology (Computer Software)

Re: For which of the following functions is f(a + b) = f(a) + f(b) for all
[#permalink]
Show Tags
22 Jun 2013, 00:44
Bunuel wrote: Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HEREWell, i did not start with picking no's or keeping the no's as a and b, But just worked in the following way : if, f(a+b) = f(a) + f(b) Then, since our answers are in this format, f(x+x) = f(x) + f(x) should also hold true, for all positive no's a and b (we havent been told that it has to be distinct, so this should be perfectly valid) Hence, you need to evaluate f(2x) here, and check weather it is equal to 2f(x) This seems to be the case only for E, hence, the answer. Quick and easy.



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1705
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: For which of the following functions is f(a + b) = f(a) + f(b) for all
[#permalink]
Show Tags
30 Sep 2014, 00:21
zz0vlb wrote: For which of the following functions is f(a+b)=f(a)+f(b) for all positive numbers a and b?
A. \(f(x)=x^2\) B. \(f(x)= x+1\) C. \(f(x) = \sqrt{x}\) D. \(f(x)=\frac{2}{x}\) E. \(f(x) = 3x\) f(a+b) = f(a) + f(b) holds true for pure multiplication with any number A: Squaring of variable.... discard B: Addition with number.... discard C: Square root..... discard D: \(\frac{2}{x} = 2 * x^{1}\) ......... power function.... discard E: Only Multiplication.... This will be the answer Answer = E



Math Expert
Joined: 02 Aug 2009
Posts: 8792

Re: For which of the following functions is f(a+b)=f(b)+f(a)
[#permalink]
Show Tags
27 Feb 2015, 02:27
sagarag wrote: For which of the following functions is F(a+b) = f(a) + f(b) for all positives numbers a and b?
A) f(x) = x^2 B) f(x) = x+1 C) f(x) = x^1/2 D) f(x) = 2/x e) f(x) = 3x hi sagar.. you can eliminate the choices by looking at the choices.. the answer cannot be a variable added or subtracted with a constant.. since that value will get added/subtracted twice on right side... B is out it cannot be a variable multiplied with another variable or with self.. A and C out.. the answer can be a variable multiplied or divided by a constant... D is out as a constant is divided by variable.. E follows the above rule ans E.. you can also find answer by testing values .. take E for example.. since f(x) = 3x, f(a) = 3a f(b) = 3b.. f(a+b)=3(a+b)=3a+(3b)=f(a)+f(b)... E is the ans
_________________



Manager
Joined: 21 Jan 2014
Posts: 93
GPA: 4

Re: For which of the following functions is f(a+b)=f(b)+f(a)
[#permalink]
Show Tags
15 Jan 2016, 06:37
Bunuel wrote: Responding to a PM. For which of the following functions is f(a+b)= f(a)+f(b) for all positive numbers a and b?A. \(f(x)=x^2\) B. \(f(x)= x+1\) C. \(f(x) = \sqrt{x}\) D. \(f(x)=\frac{2}{x}\) E. \(f(x) = 3x\) A. \(f(a+b)=(a+b)^2=a^2+2ab+b^2\neq{f(a)+f(b)}=a^2+b^2\) B. \(f(a+b)=(a+b)+1\neq{f(a)+f(b)}=a+1+b+1\) C. \(f(a+b)=\sqrt{a+b}\neq{f(a)+f(b)}=\sqrt{a}+\sqrt{b}\). D. \(f(a+b)=\frac{2}{a+b}\neq{f(a)+f(b)}=\frac{2}{a}+\frac{2}{b}\). E. \(f(a+b)=3(a+b)=3a3b=f(a)+f(b)=3a3b\). Correct. Answer: E. OR, as f(a+b)= f(a)+f(b) must be true for all positive numbers a and b, then you can randomly pick particular values of a and b and check for them: For example: \(a=2\) and \(b=3\) A. \(f(a + b) = f(5) = 5^2 = 25\neq{f(a) + f(b) = f(2) + f(3) = 2^2 + 3^2 = 13}\) B. \(f(a + b) = f(5) = 5 + 1 = 6\neq{f(a) + f(b) = f(2) + f(3) = (2 + 1) + (3 + 1) = 7}\) C. \(f(a + b)=f(5)=\sqrt{5}\neq{f(a) + f(b)=f(2)+f(3)=\sqrt{2}+\sqrt{3}}\) D. \(f(a + b)=f(5)=\frac{2}{5}\neq{f(a)+f(b)=f(2)+f(3)=\frac{2}{2}+\frac{2}{3}=\frac{5}{3}}\) E. \(f(a + b)=f(5)=3*(5) =15=f(a)+f(b)=f(2)+f(3)=3*(2)3*(3)=15\). Correct. It might happen that for some choices of a and b other options may be "correct" as well. If this happens just pick some other numbers and check again these "correct" options only. Similar questions to practice: function85751.htmlfunctionsproblemneedhelp93184.htmlletthefunctiongabfafb143311.htmlHope it helps. I always get confused with these kind of questions and I like the method to pick numbers to check whether answer choices are equal to the main statement.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10780
Location: Pune, India

Re: For which of the following functions is f(a+b)=f(b)+f(a)
[#permalink]
Show Tags
15 Jan 2016, 08:59
pepo wrote: Bunuel wrote: Responding to a PM. For which of the following functions is f(a+b)= f(a)+f(b) for all positive numbers a and b?A. \(f(x)=x^2\) B. \(f(x)= x+1\) C. \(f(x) = \sqrt{x}\) D. \(f(x)=\frac{2}{x}\) E. \(f(x) = 3x\) A. \(f(a+b)=(a+b)^2=a^2+2ab+b^2\neq{f(a)+f(b)}=a^2+b^2\) B. \(f(a+b)=(a+b)+1\neq{f(a)+f(b)}=a+1+b+1\) C. \(f(a+b)=\sqrt{a+b}\neq{f(a)+f(b)}=\sqrt{a}+\sqrt{b}\). D. \(f(a+b)=\frac{2}{a+b}\neq{f(a)+f(b)}=\frac{2}{a}+\frac{2}{b}\). E. \(f(a+b)=3(a+b)=3a3b=f(a)+f(b)=3a3b\). Correct. Answer: E. OR, as f(a+b)= f(a)+f(b) must be true for all positive numbers a and b, then you can randomly pick particular values of a and b and check for them: For example: \(a=2\) and \(b=3\) A. \(f(a + b) = f(5) = 5^2 = 25\neq{f(a) + f(b) = f(2) + f(3) = 2^2 + 3^2 = 13}\) B. \(f(a + b) = f(5) = 5 + 1 = 6\neq{f(a) + f(b) = f(2) + f(3) = (2 + 1) + (3 + 1) = 7}\) C. \(f(a + b)=f(5)=\sqrt{5}\neq{f(a) + f(b)=f(2)+f(3)=\sqrt{2}+\sqrt{3}}\) D. \(f(a + b)=f(5)=\frac{2}{5}\neq{f(a)+f(b)=f(2)+f(3)=\frac{2}{2}+\frac{2}{3}=\frac{5}{3}}\) E. \(f(a + b)=f(5)=3*(5) =15=f(a)+f(b)=f(2)+f(3)=3*(2)3*(3)=15\). Correct. It might happen that for some choices of a and b other options may be "correct" as well. If this happens just pick some other numbers and check again these "correct" options only. Similar questions to practice: function85751.htmlfunctionsproblemneedhelp93184.htmlletthefunctiongabfafb143311.htmlHope it helps. I always get confused with these kind of questions and I like the method to pick numbers to check whether answer choices are equal to the main statement. Here are a couple of posts on functions. They could help you. http://www.veritasprep.com/blog/2015/03 ... songmat/http://www.veritasprep.com/blog/2015/03 ... questions/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Re: For which of the following functions is f(a+b)=f(b)+f(a)
[#permalink]
15 Jan 2016, 08:59



Go to page
1 2
Next
[ 25 posts ]

