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f (a + b) = f (b) + f (a)

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by sanju09 » Wed Apr 08, 2009 3:27 am
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) = sqroot x

D. f (x) = 2/x

E. f (x) = -3 x


OA E
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by moutar » Wed Apr 08, 2009 3:33 am
This might not make sense.

f(a+b) = f(a) + f(b) is the definition of a linear function.

Therefore the answers can only be B or E.

f(a) + f(b) = a + b + 2 != f(a+b)

So the answer is E.

Obviously you could go through each of them with values for a and b or variables and multiply out squareds and roots.
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