Hi happygirl!

I'd start with trying to find an example where it works out.

After that we'll see.

So, suppose f(x) = C for some constant C.

Does it have an x in (0,1) such that f(x) = f(x^2)?

Suppose f(x) = |x - (1/2)|.

Does it have an x in (0,1) such that f(x) = f(x^2)?