One last one from the practice CAT

[sev]

This one really threw me off, im not even sure what the problem is asking


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


Help?

[axisymmetric]

I think the answer is (d) x^2(1-x)^2.

Replace the x in the equation to (1-x) and we will still get x^2(1-x)^2 = f(x)

[thumpin_termis]

Also another vote for d.

I picked an easy number x=1. So you have two functions to try out:

f(x) => f(1)
f(x-1) => f(1-1) = f(0)

so you have to see which of the answer choices are f(1) = f(0).

If you go through the equations in the selection and plug in both 1 and 0 for, you'll find choice d) is the only one that is equal to each other.

f(x) = x^2(1-x)^2
f(0) = 0^2(1-0)^2 = 0
f(1) = 1^2(1-1)^2 = 0

I'd think this may not be the quickest way, but it's the method that worked for me...