try plugging in numbers.. Only E satisfies the condition

Assume a =2 and b = 3

A. f(x) = x^2 (2+3)^2 (not equal to ) 2^2+3^2

B. f(x) = x+1 (2+3+1) (not equal to ) (2+1) + (3+1)

C. f(x) = √x sq toot 5 (not equal to ) sqrt 2+ sq rt 3

D. f(x) = 2/x 2/ (2+3) (not equal to ) 2/2 + 2/3

E. f(x) = -3x -3(2+3) is equal to -3(2) + -3(3)

hence it satisifes the condition..

Hope its clear...

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) = √x
D. f(x) = 2/x
E. f(x) = -3x

This concept seems to be tested frequently. You should recognize the pattern
a(b+c) = ab + ac, which is the distributive property. The operation you are looking for is multiplication. Since E is the only choice that represent multiplication E is the right answer.

thanks for the responses