Gmat prep functions

[awilhelm]

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)

How should I approach these types of problems?

[aroon7]

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)

How should I approach these types of problems?

substitute x as 1-x in the functions and check if it is equal to function f(x)

a) f(1-x) = 1-(1-x) = -x
b) f(1-x) = 1-(1-x)^2 = 1-(1+x^2 - 2x)
c) f(1-x) = (1-x)^2 - (1-(1-x)^2) = (1+ x^2 -2x) - (1-X^2-1+2x)
d) f(1-x) = (1-x)^2 (1-(1-x))^2 = x^2 (1-x)^2 = f(x)

ans is D

[awilhelm]

Would you mind showing algebraically how you reduced answer D to arrive at x^2(1-x)^2?

[sanjay_dce]

Would you mind showing algebraically how you reduced answer D to arrive at x^2(1-x)^2?

put x = 1-x and hence f(1-x)= (1-x)^2 ( 1-(1-x)) ^2= (1-x)^2 (x)^2 = f(x) hope its clear now

[awilhelm]

Yes, definitely. My mistake.