For which of the following functions f is f(x)=f(1-x) for

[GMAT 5/18]

No idea on where to even begin!

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)

[dbernst]

I approached this as a VIC problems, so I decided to plug in values for x. I'm not certain that this is the BEST approach, but it is one approach. I chose the number 2 for x and thus -1 for 1-x. Then, I tested each answer choice.

a. f(x) = 1-x
a. f(2) = -1; f(-1) = 2. Eliminate a.
b. f(x) = 1-x^2
b. f(2) = -3; f(-1) = 0. Eliminate b.
c. f(x) = x^2 - (1-x)^2
c. f(2) = 3; f(-1) = -3. Eliminate c
d. f(x) = x^2(1-x)^2
d. f(2) = 4; f(-1) = 4. Keep d.
e. f(x) = x / (1-x)
e. f(2) = -2; f(-1) = -1/2. Eliminate e.

The correct answer is D.

[GMAT750]

Thanks, Dan.

I think the most challenging part of that question, for me, was understanding what the GMAC was asking!

[swarbhanu_handique]

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

[RonPurewal]

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

yep. that's the theory way to understand the question.

the vic approach, as noted by dan above, is probably easier - but, if you're good enough at theory and algebra, then this works too.