7. If f is continuous on [0, 1] and if [s f(x)x" dx = 0 (n = 0, 1, 2, ...), prove that f(x) = 0 on [0, 1]. Hint: The integral of the product of f with any polynomial is zero. Use the Weierstrass theorem to show that f f(x) dx = 0.

Let f : I → J be a bijective differentiable function froman interval I to an interval J, and let F : I → R be an anti-derivative of f. Find an explicit expression, in terms of f, f-1 and F, for an anti-derivative of f-1: J → I. [Both substitution and integration by parts may come in handy.]

I need the next 3 parts pls!

Suppose that the function f: R → R has the property that -x2 <ƒ(x)