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by emiflo » Sat Aug 07, 2010 5:07 am
Hi guys could someone please explain the answer to this question

For which of the following functions f 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

ps. the ans is D
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by selango » Sat Aug 07, 2010 5:16 am
f(x)=f(1-x)

for f(1-x) sub x=(1-x) in the value of the function.

A.

f(x)=1-x
f(1-x)=1-(1-x)=x

f(x)!=f(1-x)

B.

f(X)=1-x^2
f(1-x)=1-(1-x)^2=1-(x^2-2x+1)=2x-x^2

f(x)!=f(1-x)

C.

f(X)=x^2-(1-x)^2
f(1-x)=(1-x)^2-x^2

f(x)!=f(1-x)

D.

f(X)=x^2(1-X)^2
f(1-x)=(1-x)^2.x^2=x^2.(1-x)^2

As you can see f(x)=f(1-x)

Pick D

Hope this clarify..
--Anand--
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by gmatmachoman » Sat Aug 07, 2010 5:27 am
emiflo wrote:Hi guys could someone please explain the answer to this question

For which of the following functions f 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

ps. the ans is D
replace X by (1-X) in the options to check where f(x)= f(1-x).

Option D : f(X)=x^2(1-X)^2
After replacing X with (1-X) : (1-X)^2 ( 1- (1-X))^2
(1-X)^2 (X) ^2
This is same as f(X).
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