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i can think of the identity function f(x) = x

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) =...