For which of the following functions is f (x) = f (1 - x) for all x?
(A) f (x) = 1 - x
(B) f (x) = 1 - x^2
(C) f (x) = x^2 - (1 - x) ^2
(D) f (x) = x^2 (1 - x) ^2
(E) f (x) = x/(1 - x)
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f (x) = f (1 – x) for all x
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sanju09
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liferocks
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putting x=1-x ans options will become like this
[spoiler](A) f (x) = 1 - x or f(1-x)=x
(B) f (x) = 1 - x^2 or f(1-x)=1-(1-x)^2
(C) f (x) = x^2 - (1 - x) ^2 or f(1-x)=(1-x)^2-x^2=-f(x)
(D) f (x) = x^2 (1 - x) ^2 or f(1-x)= (1 - x) ^2x^2 =f(x)..correct
(E) f (x) = x/(1 - x) or f(1-x)=(1-x)/x[/spoiler]
[spoiler](A) f (x) = 1 - x or f(1-x)=x
(B) f (x) = 1 - x^2 or f(1-x)=1-(1-x)^2
(C) f (x) = x^2 - (1 - x) ^2 or f(1-x)=(1-x)^2-x^2=-f(x)
(D) f (x) = x^2 (1 - x) ^2 or f(1-x)= (1 - x) ^2x^2 =f(x)..correct
(E) f (x) = x/(1 - x) or f(1-x)=(1-x)/x[/spoiler]
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Patrick_GMATFix
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The key is to understand that in the correct answer (function) if we replace x with (1-x) and simplify the expression, it should come out to be the same as the original.
An alternative way is to plug in a value for x into each function and plug in the corresponding value for 1-x. The two should equal each other. For instance, if we plug in x=0, then f(x)=f(0) and f(1-x)=f(1). In the correct answer, f(x)=f(1-x) --> f(0)=f(1).
The correct answer is D. This is QID 1142
-Patrick
An alternative way is to plug in a value for x into each function and plug in the corresponding value for 1-x. The two should equal each other. For instance, if we plug in x=0, then f(x)=f(0) and f(1-x)=f(1). In the correct answer, f(x)=f(1-x) --> f(0)=f(1).
The correct answer is D. This is QID 1142
-Patrick
