|
Author |
Message |
|
TAGS:
|
|
|
Manager
Joined: 27 Feb 2010
Posts: 107
Location: Denver
Followers: 1
Kudos [?]:
71
[1] , given: 14
|
For which of the following functions is f(a+b)=f(a)+f(b) for [#permalink]
 23 Apr 2010, 16:24
1
This post received
KUDOS
Question Stats:
72% (01:55) correct
27% (00:49) wrong based on 70 sessions
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^2B. f(x)= x+1C. f(x) = \sqrt{x}D. f(x)=\frac{2}{x}E. f(x) = -3xSomeone please provide me the solution for this problem.
|
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12096
Followers: 1876
Kudos [?]:
10096
[6] , given: 959
|
Re: functions Problem need help. [#permalink]
24 Apr 2010, 07:02
6
This post received
KUDOS
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^2B. f(x)= x+1C. f(x) = \sqrt{x}D. f(x)=\frac{2}{x}E. f(x) = -3xA. f(a+b)=(a+b)^2=a^2+2ab+b^2\neq{f(a)+f(b)}=a^2+b^2B. f(a+b)=(a+b)+1\neq{f(a)+f(b)}=a+1+b+1C. 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)=-3a-3b=f(a)+f(b)=-3a-3b. 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=3A. 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.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!, 11 New DS set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Joined: 27 Feb 2010
Posts: 107
Location: Denver
Followers: 1
Kudos [?]:
71
[0], given: 14
|
Re: functions Problem need help. [#permalink]
24 Apr 2010, 10:23
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: 220
Followers: 1
Kudos [?]:
15
[0], given: 8
|
Re: functions Problem need help. [#permalink]
24 Apr 2010, 10:36
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^2B. f(x)= x+1C. f(x) = \sqrt{x}D. f(x)=\frac{2}{x}E. f(x) = -3xA. f(a+b)=(a+b)^2=a^2+2ab+b^2\neq{f(a)+f(b)}=a^2+b^2B. f(a+b)=(a+b)+1\neq{f(a)+f(b)}=a+1+b+1C. 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)=-3a-3b=f(a)+f(b)=-3a-3b. 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=3A. 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
_________________
Success is my Destiny
|
|
|
|
|
|
Intern
Joined: 21 Apr 2010
Posts: 7
Followers: 0
Kudos [?]:
1
[1] , given: 6
|
Re: functions Problem need help. [#permalink]
24 Apr 2010, 15:51
1
This post received
KUDOS
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^2B. f(x)= x+1C. f(x) = \sqrt{x}D. f(x)=\frac{2}{x}E. f(x) = -3xA. f(a+b)=(a+b)^2=a^2+2ab+b^2\neq{f(a)+f(b)}=a^2+b^2B. f(a+b)=(a+b)+1\neq{f(a)+f(b)}=a+1+b+1C. 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)=-3a-3b=f(a)+f(b)=-3a-3b. 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=3A. 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: 04 May 2010
Posts: 89
WE 1: 2 yrs - Oilfield Service
Followers: 8
Kudos [?]:
45
[1] , given: 7
|
1
This post received
KUDOS
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 ( )
|
|
|
|
|
|
Ms. Big Fat Panda
Status: Biting Nails Into Oblivion
Joined: 09 Jun 2010
Posts: 1858
Followers: 296
Kudos [?]:
1126
[1] , given: 194
|
Re: gmat prep test [#permalink]
15 Jun 2010, 06:22
1
This post received
KUDOS
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.
|
|
|
|
|
|
Intern
Joined: 16 Dec 2010
Posts: 7
Followers: 0
Kudos [?]:
1
[0], given: 1
|
Re: functions Problem need help. [#permalink]
30 Dec 2010, 02:38
i think Karishma has explained very good point to tackle these functions problems, As per her explanation we should first try options with multiple , divide add and then subtract…. So trying option E was obvious and it fits well… saves time indeed…
Ans E
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12096
Followers: 1876
Kudos [?]:
10096
[0], given: 959
|
Re: gmat prep test [#permalink]
30 Dec 2010, 15:41
marijose wrote: whiplash2411 wrote: 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. Is there a way to solve the problem without doing all the calculations? Basically there are 2 approaches possible: algebraic and number plugging, check my post for both.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!, 11 New DS set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12096
Followers: 1876
Kudos [?]:
10096
[1] , given: 959
|
Re: Gmat Prep Functions VIC problem [#permalink]
03 Jan 2011, 02:38
1
This post received
KUDOS
|
|
|
|
|
|
Manager
Status: Waiting on 2nd round decisions from Wharton, Kellogg, and Booth. Received CGSM Fellowship Award offer to Haas!
Joined: 19 Nov 2009
Posts: 128
Concentration: General Management, Entrepreneurship
GMAT 1: 710 Q48 V39
Followers: 5
Kudos [?]:
32
[0], given: 209
|
Re: functions Problem need help. [#permalink]
03 Jan 2011, 20:52
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^2B. f(x)= x+1C. f(x) = \sqrt{x}D. f(x)=\frac{2}{x}E. f(x) = -3xA. f(a+b)=(a+b)^2=a^2+2ab+b^2\neq{f(a)+f(b)}=a^2+b^2B. f(a+b)=(a+b)+1\neq{f(a)+f(b)}=a+1+b+1C. 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)=-3a-3b=f(a)+f(b)=-3a-3b. 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=3A. 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.
|
|
|
|
|
|
|
Re: functions Problem need help.
[#permalink]
03 Jan 2011, 20:52
|
|
|
|
|
|
|
|
|
|
|
close
