For which of the following functions is f(a+b)=f(b)+f(a) : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 21 Jan 2017, 23:40

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# For which of the following functions is f(a+b)=f(b)+f(a)

Author Message
TAGS:

### Hide Tags

Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 536
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 74

Kudos [?]: 2972 [3] , given: 217

For which of the following functions is f(a+b)=f(b)+f(a) [#permalink]

### Show Tags

12 Dec 2011, 05:52
3
KUDOS
57
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

72% (01:54) correct 28% (00:48) wrong based on 906 sessions

### HideShow timer Statistics

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?
[Reveal] Spoiler: OA

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93382 [38] , given: 10557

### Show Tags

15 Jan 2012, 15:06
38
KUDOS
Expert's post
48
This post was
BOOKMARKED
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. $$f(a+b)=-3(a+b)=-3a-3b=f(a)+f(b)=-3a-3b$$. Correct.

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:
function-85751.html
functions-problem-need-help-93184.html
let-the-function-g-a-b-f-a-f-b-143311.html

Hope it helps.
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7125
Location: Pune, India
Followers: 2137

Kudos [?]: 13688 [9] , given: 222

Re: For which of the following functions is f(a+b)=f(b)+f(a) [#permalink]

### Show Tags

16 Jan 2012, 01:00
9
KUDOS
Expert's post
5
This post was
BOOKMARKED
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
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 12 Jul 2011 Posts: 151 Concentration: Operations, Strategy GMAT 1: 680 Q46 V37 WE: Engineering (Telecommunications) Followers: 1 Kudos [?]: 35 [4] , given: 42 Re: function F(x) [#permalink] ### Show Tags 12 Dec 2011, 06:47 4 This post received KUDOS 1 This post was BOOKMARKED 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. Manager Joined: 09 Nov 2011 Posts: 129 Followers: 1 Kudos [?]: 54 [2] , given: 16 Re: function F(x) [#permalink] ### Show Tags 22 Dec 2011, 09:08 2 This post received KUDOS 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.. _________________ Time to play the game... Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7125 Location: Pune, India Followers: 2137 Kudos [?]: 13688 [2] , given: 222 Re: For which of the following functions is f(a+b)=f(b)+f(a) [#permalink] ### Show Tags 15 Jan 2016, 08:59 2 This post received KUDOS Expert's post 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. $$f(a+b)=-3(a+b)=-3a-3b=f(a)+f(b)=-3a-3b$$. 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 $$b=3$$ 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: function-85751.html functions-problem-need-help-93184.html let-the-function-g-a-b-f-a-f-b-143311.html Hope 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 ... s-on-gmat/ http://www.veritasprep.com/blog/2015/03 ... questions/ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 100

Kudos [?]: 892 [1] , given: 43

### Show Tags

07 Sep 2012, 22:17
1
KUDOS
BigUp wrote:
Hello GmatClub,

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 $$-3a-3b=-3a-3b$$ YES!!!

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 25

Kudos [?]: 433 [1] , given: 11

For which of the following functions is f(a+b)=f(b)+f(a) [#permalink]

### Show Tags

20 Dec 2012, 22:06
1
KUDOS
1
This post was
BOOKMARKED
Best to answer this with tiny-winie 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!

_________________

Impossible is nothing to God.

Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93382 [0], given: 10557

Re: For which of the following functions is f(a+b)=f(b)+f(a) [#permalink]

### Show Tags

08 Jul 2013, 00:10
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

To find DS questions by Kudos, sort by Kudos here: gmat-data-sufficiency-ds-141/
To find PS questions by Kudos, sort by Kudos here: gmat-problem-solving-ps-140/

_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13493
Followers: 576

Kudos [?]: 163 [0], given: 0

Re: For which of the following functions is f(a+b)=f(b)+f(a) [#permalink]

### Show Tags

09 Dec 2014, 10:41
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Verbal Forum Moderator
Joined: 02 Aug 2009
Posts: 4238
Followers: 329

Kudos [?]: 3461 [0], given: 101

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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Manager
Joined: 21 Jan 2014
Posts: 105
GMAT 1: 500 Q32 V28
GPA: 4
Followers: 3

Kudos [?]: 17 [0], given: 46

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. $$f(a+b)=-3(a+b)=-3a-3b=f(a)+f(b)=-3a-3b$$. Correct.

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:
function-85751.html
functions-problem-need-help-93184.html
let-the-function-g-a-b-f-a-f-b-143311.html

Hope 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.
Intern
Joined: 24 Mar 2016
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: For which of the following functions is f(a+b)=f(b)+f(a) [#permalink]

### Show Tags

24 Mar 2016, 03:54
For which of the following functions is f(a+b)=f(a)f(b) for all real numbers a and b?
A) f(x) = sin(x )
B) f( x) =log3x
C) f( x) =e^x
D) f(x)= x
Verbal Forum Moderator
Joined: 02 Aug 2009
Posts: 4238
Followers: 329

Kudos [?]: 3461 [0], given: 101

Re: For which of the following functions is f(a+b)=f(b)+f(a) [#permalink]

### Show Tags

24 Mar 2016, 04:06
For which of the following functions is f(a+b)=f(a)f(b) for all real numbers a and b?
A) f(x) = sin(x )
B) f( x) =log3x
C) f( x) =e^x
D) f(x)= x

Hi,

firstly the trignometric expressions are not tested in GMAT
secondly, pl post new topics separately by following guidelines
if f( x) =e^x
f( a) =e^a
f( b) =e^b..
so f(a)f(b)= e^a*e^b= e^(a+b)= f(a+b)
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93382 [0], given: 10557

Re: For which of the following functions is f(a+b)=f(b)+f(a) [#permalink]

### Show Tags

24 Mar 2016, 04:13
For which of the following functions is f(a+b)=f(a)f(b) for all real numbers a and b?
A) f(x) = sin(x )
B) f( x) =log3x
C) f( x) =e^x
D) f(x)= x

This is NOT a GMAT question. So, you can ignore it.
_________________
Senior Manager
Affiliations: Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 310
GMAT 1: 770 Q47 V48
WE: Education (Education)
Followers: 45

Kudos [?]: 266 [0], given: 42

For which of the following functions is f(a+b)=f(b)+f(a) [#permalink]

### Show Tags

06 Apr 2016, 12:23
1
This post was
BOOKMARKED
Attached is a visual that should help. Alternate method: plug in a=1 and b=1 to make the math easier.
Attachments

Screen Shot 2016-08-04 at 6.53.30 PM.png [ 112.94 KiB | Viewed 15523 times ]

Screen Shot 2016-08-04 at 7.22.53 PM.png [ 792.38 KiB | Viewed 15530 times ]

IMG_1002.JPG [ 324.37 KiB | Viewed 15511 times ]

_________________

Harvard grad and 770 GMAT scorer, offering high-quality private GMAT tutoring, both in-person and via Skype, since 2002.

McElroy Tutoring

Intern
Joined: 19 Aug 2016
Posts: 21
Followers: 0

Kudos [?]: 2 [0], given: 0

For which of the following functions is [#permalink]

### Show Tags

19 Jan 2017, 04:31
i face difficulty in solving these kind of questions. can someone suggest a particular methodology for these questions?

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{m}

D. f(x) = 2/x

E. f(x) = -3x
Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93382 [0], given: 10557

Re: For which of the following functions is f(a+b)=f(b)+f(a) [#permalink]

### Show Tags

19 Jan 2017, 04:48
ashikaverma13 wrote:
i face difficulty in solving these kind of questions. can someone suggest a particular methodology for these questions?

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{m}

D. f(x) = 2/x

E. f(x) = -3x

Merging similar questions. Please refer to the solutions above.

P.S. Please search before posting and provide the OA along with a question. Check rules here: rules-for-posting-please-read-this-before-posting-133935.html
_________________
Re: For which of the following functions is f(a+b)=f(b)+f(a)   [#permalink] 19 Jan 2017, 04:48
Similar topics Replies Last post
Similar
Topics:
7 Among the following functions, for which one is 8 10 Aug 2013, 09:20
13 For which of the following functions is g(c-d) = g(c) - g(d) 9 11 Feb 2013, 09:09
2 For which of the following functions f is f(x) = f(1-x) for 15 28 Jun 2011, 07:12
50 For which of the following functions is f(a+b)=f(a)+f(b) for 16 23 Apr 2010, 15:24
220 For which of the following functions f is f(x)=f(1-x) for 32 25 Oct 2009, 01:34
Display posts from previous: Sort by