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my first function question ever!

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my first function question ever!

by akane » Sun Nov 06, 2011 5:49 am
For which of the following functions is f(a+b)= f(a)+f(b) for all positive numbers a and b. I would like to know the reasoning to solve this,because I have never encountered a function question before
Thanks for your posts!
Choices:
f(x)=x^2
f(x)=x+1
f(x)=Vx
f(x)=2/x
f(x)=-3x
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by shankar.ashwin » Sun Nov 06, 2011 6:33 am
Choice 1

f(a) = a^2 and f(b) = b^2 -> f(a) + f(b) = a^2 + b^2
F(a+b) = (a+b) ^2

Choice 2

f(a) = a+1 and f(b) = b+1 -> f(a)+f(b) = a+b+2
f(a+b) = a+b+1

Choice 3

f(a) = Va and f(b) = Vb -> f(a)+f(b)=V(a)+v(b) (v-sqrt)
f(a+b) = v(a+b)

Choice 4

f(a) = 2/a and f(b)=2/b -> f(a)+f(b) = 2/a + 2/b

Choice 5
f(a) = -5a and f(b) = -5b -> f(a)+f(b) = -5(a+b)
f(a+b) = -5(a+b)

Only E satisfies
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