Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 27 Oct 2016, 21:04

### 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) for

Author Message
TAGS:

### Hide Tags

Manager
Joined: 05 Jul 2006
Posts: 197
Followers: 1

Kudos [?]: 59 [0], given: 0

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

### Show Tags

30 Aug 2006, 11:33
2
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

67% (02:09) correct 33% (01:17) wrong based on 299 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: for-which-of-the-following-functions-is-f-a-b-f-b-f-a-124491.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Jul 2014, 13:57, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
CEO
Joined: 20 Nov 2005
Posts: 2911
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 23

Kudos [?]: 260 [0], given: 0

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

### Show Tags

30 Aug 2006, 11:47
2
This post was
BOOKMARKED
lan583 wrote:
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. of x
f(x)= 2/x
f(x)=-3x

Straight E.

1. (a+b)^2 a^2+b^2
2. a+b+1 (a+1) + (b+1)
3. √(a+b) √a + √b
4. 2/(a+b) 2/a + 2/b
5. -3(a+b) = -3a + (-3b)
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12266
Followers: 542

Kudos [?]: 151 [0], given: 0

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

### Show Tags

28 Jul 2014, 13:48
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.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 35326
Followers: 6649

Kudos [?]: 85882 [0], given: 10258

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

### Show Tags

28 Jul 2014, 13:59
Expert's post
1
This post was
BOOKMARKED
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:
for-which-of-the-following-functions-f-is-f-x-f-1-x-for-85751.html
for-which-of-the-following-functions-is-f-a-b-f-a-f-b-for-93184.html
let-the-function-g-a-b-f-a-f-b-143311.html

Check other function questions in our Special Questions Directory:

Operations/functions defining algebraic/arithmetic expressions
Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions

OPEN DISCUSSION OF THIS QUESTION IS HERE: for-which-of-the-following-functions-is-f-a-b-f-b-f-a-124491.html
_________________
Re: For which of the following functions is f(a+b)=f(b)+f(a) for   [#permalink] 28 Jul 2014, 13:59
Similar topics Replies Last post
Similar
Topics:
7 Among the following functions, for which one is 8 10 Aug 2013, 10:20
152 For which of the following functions is f(a+b)=f(b)+f(a) 17 12 Dec 2011, 06:52
2 For which of the following functions f is f(x) = f(1-x) for 15 28 Jun 2011, 08:12
40 For which of the following functions is f(a+b)=f(a)+f(b) for 16 23 Apr 2010, 16:24
204 For which of the following functions f is f(x)=f(1-x) for 32 25 Oct 2009, 02:34
Display posts from previous: Sort by