these are questions from Calculus by spivak 3rd edition.
7) How many continuous functions f are there which satisfy (f(x))^2= x^2 for all x?
8) Suppose that f and g are continuous, and that f^2 = g^2, and that f(x) ≠ 0 for all x. Prove that either f(x) = g(x) for all x, or else f(x) =...