I'm not sure how to deal with this type of exercises. Here is what I solved so far:

1.



if x=0 and if x>0
Is this possible? I don't think it's correct.

2.



What should I do next?

For question 1, it seems to me that if x = 1 it would also satisfy the equations. But in general the conclusion that f(x) = f(x^4) applies only if f(x) = f(x^2) throughout the entire domain of x. That leads me to believe that this only works if f(x) = C (a constant).

There are pleanty fop functions where f(x) = f(x^2) for some values of x, but f(x^2) does not equal f(x^4). For example: if f(x) = sin(x), then for . For n = 1 this results in



but


For 2: if you take log base 2 of both sides then x = x log3, so x = 0. Or again, perhaps f(x) = C.