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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

Deja vu! Here's another function question from the GMAT prep. If you want to check out another solution for a functions question before tackling this one go here: For which of the following functions f(x)=f(1-x)

Again, function questions generally look harder than they are. The first read is usually confusing. Just keep in mind that the premise is simple. For this one: find the answer choice for which plugging in a + b into the function is the same as plugging in a then plugging in b and summing the outcome. Let's just go through the answer choices. I would pick values for a and b. Let's go for a = 2, b = 3. Just a recap we want f(2 + 3) = f(2) + f(3). You can find a video explanation here: 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

5^2 vs 3^2 + 2^2

25 vs 13

 

B. f(x) = x+1

5 + 1 vs (2+1) + (3+1)

6 vs 7

C. f(x) = √x

√5 vs. √2 + √3

√5 is less than 3. √2 is about 1.4, √4 is about 1.7 so their sum is more than 3.

 

D. f(x) = 2/x

2/5 vs 2/2 + 2/3

The right side is clearly bigger.

 

E. f(x) = -3x

-3(5) vs -3(2) + -3(3)

-15 = -15

 

for which of the following functions is f(a+b)

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