GMATPrep

[diegoasaavedra]

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

Answer is D, can some body help with this?

Thanks

[sanju09]

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

Answer is D, can some body help with this?

Thanks

Check one by one the choices...

A. If f(x) = 1 - x, then f (1 - x) = 1 - (1 - x) = x; not the same.

B. If f(x) = 1 - x^2, then f (1 - x) = 1 - (1 - x) ^2 = 2 x - x^2; not the same.

C. If f(x) = x^2 - (1 - x) ^2 = 2 x - 1, then f (1 - x) = (1 - x) ^2 - x^2 = 1 - 2 x; not the same.

D. If f(x) = x^2 (1 - x) ^2, then f (1 - x) = (1 - x) ^2 (1 - 1 + x) ^2 = x^2 (1 - x) ^2; the same.

E. Ignore E.

[spoiler]Take D[/spoiler]

[GMATGuruNY]

I posted an alternate solution here:

https://www.beatthegmat.com/gmatprep-fun ... 66593.html