I posted a solution here:
https://www.beatthegmat.com/for-which-of ... 65920.html

rsarashi 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) = x²

B) f(x) = x+1

C) f(x) = under root x

D) f(x) = 2/x

E) f(x) = -3x

OAE[/spoiler]

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(s) 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) = √x

f(3) = √3

f(1) = √1 = 1

f(2) = √2

Since √3 does not equal 1 + √2, 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