f(a+b)=f(a)+f(b)

Expert replies

dzelkas: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Tue Jun 05, 2007 1:29 pm

by dzelkas » Wed Jul 04, 2007 2:30 pm

can someone help me explain how to solve this problem?

For which of the following functions is f(a+b)=f(a)+f(b) for al positive numbers a and b?

a) f(x)=x^2

b) f(x)=x+1

c) f(x)= sq root of x

d) f(x)=2/3

e) f(x)=-3x

Like this post

Source: Beat The GMAT — Problem Solving | Wed Jul 04, 2007 2:30 pm

tinni: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Wed Jun 27, 2007 12:45 pm; Thanked: 1 times

Re: f(a+b)=f(a)+f(b)

by tinni » Wed Jul 04, 2007 2:51 pm

dzelkas wrote:can someone help me explain how to solve this problem?

For which of the following functions is f(a+b)=f(a)+f(b) for al positive numbers a and b?

a) f(x)=x^2

b) f(x)=x+1

c) f(x)= sq root of x

d) f(x)=2/3

e) f(x)=-3x

I will go by each option:

from (A) : f(a)=a^2 , f(b)=b^2 f(a+b)=(a+b)^2 which is not equal to (a^2) + (b^2) [ f(a) + f(b) ]

from (B): f(a)=a+1 , f(b)=b+1 , f(a+b)=a+b+1 which is not equal to (a+1)+(b+1) = a+b+2 [ f(a) + f(b) ]

from (C): f(a)= sqrt(a) , f(b)=sqrt(b) , f(a+b) = sqrt(a+b ) which is not equal to sqrt(a)+sqrt(b) [ f(a) + f(b) ]

from (D) : f(a)=2/3 , f(b) = 2/3 , f(a+b)=2/3 which is not equal to 2/3 + 2/3 [ f(a) + f(b) ]

from (E): f(a)= -3a , f(b)= -3b , f(a+b)= -3(a+b)=(-3a) + (-3b)=f(a) + f(b)

Hence, (E) will be my answer.

Like this post

casbroker: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Sun Oct 14, 2007 2:08 pm

by casbroker » Sun Oct 21, 2007 5:03 pm

Thanks for that - I had a similar question and had no clue where to start.

Like this post

jazzcat4u: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Mon May 12, 2008 2:43 pm

by jazzcat4u » Thu Sep 25, 2008 10:04 am

I'm still lost on this one..how do you rephrase what this question is asking?

For which of the following functions is f(a+b)=f(a)+f(b) for all positive numbers a and b?

Can you intepret it as asking for all of the functions below, which function, that is the sum of 2 numbers produces an output that is equal to the sum of those 2 numbers' functions? I'm confused...just trying to put this math into simple english...

Like this post

Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Dec 11, 2017 11:30 am

dzelkas wrote:can someone help me explain how to solve this problem?

For which of the following functions is f(a+b)=f(a)+f(b) for al positive numbers a and b?

a) f(x)=x^2

b) f(x)=x+1

c) f(x)= sq root of x

d) f(x)=2/3

e) f(x)=-3x

We need to determine when f(a + b) = f(a) + f(b). We can determine the correct answer choice by substituting numerical values for a and b. We could use any two values for a and b, but for simplicity, let's choose a = 1 and b = 2. The function now looks like this:

f(1 + 2) = f(1) + f(2)

f(3) = f(1) + f(2)

So, we must determine which answer choice has f(3) equal to the sum of f(1) and f(2).

Let's evaluate each answer choice.

A) f(x) = x^2

f(3) = 3^2 = 9

f(1) = 1^2 = 1

f(2) = 2^2 = 4

Since 9 does not equal 1 + 4, choice A is not correct.

B) f(x) = x + 1

f(3) = 3 + 1 = 4

f(1) = 1 + 1 = 2

f(2) = 2 + 1 = 3

Since 4 does not equal 3 + 2, choice B is not correct.

C) f(x) = âˆšx

f(3) = âˆš3

f(1) = âˆš1 = 1

f(2) = âˆš2

Since âˆš3 does not equal 1 + âˆš2, choice C is not correct.

D) f(x) = 2/x

f(3) = 2/3

f(1) = 2/1 = 2

f(2) = 2/2 = 1

Since 3/2 does not equal 1 + 2, choice D is not correct.

E) f(x) = -3x

f(3) = -3(3) = -9

f(1) = -3(1) = -3

f(2) = -3(2) = -6

Since -9 equals -3 + (-6), choice E is correct.

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review