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need help understanding question about functions

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need help understanding question about functions [#permalink] New post 23 Jun 2010, 20:18
can anyone help me understand how to solve this problem? it's from the gmat club test #25, question #22. the explanation doesn't quite make sense to me. thanks in advance :)

if function f(x) satisfies f(x)=f(x^2) for all x, which of the following must be true?

a. f(4)=f(2)f(2)
b. f(16)-f(-2)=0
c. f(-2)+f(4)=0
d. f(3)=3f(3)
e. f(0)=0
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Re: need help understanding question about functions [#permalink] New post 23 Jun 2010, 23:18
The function is such that f(x) = f(x^2) This means it has the same value for a number and its square.

When testing choices, always start with E

E. f(0) , we can only say that this is equal to f(0^2) = f(0) . So this need not be = 0.

D. f(3) = f(9). This does not mean it is equal to 3*f(3) as we do not know the value of either f(3) or f(9), just that they are equal.

C. f(-2) = f( -2^2) = f(4) => f(-2) - f(4) = 0, but this doesn't tell us the value of f(-2) + f(4).

B. f(-2) = f(-2^2) = f(4) = f(4^2) = f(16) therefore f(16) - f(-2) = 0 , since they are both equal

Pick B.
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Re: need help understanding question about functions [#permalink] New post 24 Jun 2010, 08:21
thank you! I also found the posts explaining the gmat club test questions, and these are all very helpful :)
Re: need help understanding question about functions   [#permalink] 24 Jun 2010, 08:21
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