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

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For which of the following functions is f(a+b)=f(a)+f(b) for [#permalink]  29 Jul 2007, 11:01
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+2
C. f(x)=square root x (not sure symbol for root)
D. f(x)=2/x
E. f(x)=3x
Senior Manager
Joined: 06 Mar 2006
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f(x)=3x

f(a)=3a and f(b)=3b f(a)+f(b)=3a+3b
f(a+b)=3(a+b)=3a+3b,

therefore f(a+b)=f(a)+f(b) when f(x)=3x
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