BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pm
Thanked: 6 times
Followed by:5 members

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

by Vincen » Fri May 28, 2021 6:50 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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. \(f(x)=\dfrac2{x}\)

E. \(f(x)=-3x\)

Answer: E

Source: GMAT Prep
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

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

by Brent@GMATPrepNow » Sat May 29, 2021 4:09 am
Vincen wrote: ↑
Fri May 28, 2021 6:50 am
 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. \(f(x)=\dfrac2{x}\)

E. \(f(x)=-3x\)

Answer: E

Source: GMAT Prep
One approach is to plug in numbers. Let's let a = 1 and b = 1

So, 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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1