pls explain?

Question

how many continous real valued functions f are there with domain [-1,1] such that (f(x))^2=x^2 for each x in [-1,1]

Answer 1

I would say two: f(x) = x and f(x) = -x.

If you take the square root of both sides, that's what you get. And I can't think of any other way to generate such a function. Squaring f(x) can only produce x^2 if f(x) is a square root of x^2. And the two square roots of x^2 are x and -x.

Answer 2

4, x, -x, |x| and -|x|