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# unsolved challenge problem

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Director
Joined: 09 Aug 2006
Posts: 525
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Kudos [?]: 39 [0], given: 0

unsolved challenge problem [#permalink]  22 Jul 2007, 04:58
Hi Guys,
the problem in below has not reached a conclusion on why E is wrong. could anyone help..

http://www.gmatclub.com/phpbb/viewtopic ... =challenge
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Manager
Joined: 08 Jul 2007
Posts: 174
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Kudos [?]: 5 [0], given: 0

function f (x) SATISFIES f (x) =f (x)^2 FOR ALL x which of the following must be true

f(4) = f(2)*f(2)
f(16) - f(-2) = 0
f(-2) + f(4) = 0
f(3) = 3*f(3)
f(0) = 0

E is not necessarily true. It depends on the function. For example, if the function were such that f(x)=1 for all values of x, then f(x)=f(x)^2 but f(x) does not equal 0. Does that make sense? We have no function so we can't assume that f(0)=0. f(0) could equal some other value depending on the function.
Director
Joined: 14 Jan 2007
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No numerical value of f(x) can be derived from the question. Stem states the values of function in terms of function.
Senior Manager
Joined: 28 Jun 2007
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Yeah... consider an example:

f(x) = x+1

f(0) != 0.

f(0) = 1.

Though its not one of those examples that satisfies your equation, I guess it proves that the assumption of f(0)=0 is wrong if there is a constant in the equation.
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