# Math Help - F of x Function Problem Please See Test Tomorrow

1. ## F of x Function Problem Please See Test Tomorrow

How would you evaluate and substitute this problem.

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

This is just a little too long ago for me to remember. I just need to see how you substitute and evaluate. If you could work it out so I could see, that would be epic win. Thanks guys.

2. Originally Posted by dapefley
How would you evaluate and substitute this problem.

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

This is just a little too long ago for me to remember. I just need to see how you substitute and evaluate. If you could work it out so I could see, that would be epic win. Thanks guys.
Which functions are we choosing from?

3. Thats just it, there is nothing to choose from. I know the answer is
f(x)=x^2(1-x)^2...
I just need to see how to get there....

5. HAHA... I know right...
the thing is I am taking a practice test for the GMAT on the computer and it is telling me the answer to the question is f(x)=x^2(1-x)^2....IDK...
is there any way to get to that anwer with what is given??

6. No, if you're asked to choose from some possible answers, and you haven't been given any answers to choose from, you can't possibly choose an answer.

7. Alright, well thanks anyway... I guess it was just a typo in the practice test..lol.. thanks again.

8. Originally Posted by Prove It
No, if you're asked to choose from some possible answers, and you haven't been given any answers to choose from, you can't possibly choose an answer.
In which case, the question is:

Find a function that satisfies f(x) = f(1 - x) for all values of x.

9. I think what dapefley is saying is that the question was to determine which of several given functions (which he apparently does not remember) satisfies f(x)=f(1-x) for all x and that the "correct" answer was then given as $f(x)= x^2(1- x)^2$.

You determine that by doing what it says and seeing if the equation is true. In particular you find f(1- x) by replacing the "x" in the formula by 1-x: $f(x)= x^2(1- x)^2$ so $f(1- x)= (1-x)^2(1- (1-x))^2$. Of course, 1-(1-x)= 1-1+x= x so $f(1-x)= (1-x)^2x^2= f(x)$.