Let A = (-1, o0). Suppose that f: A R is a differentiable function with the...

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Let A = (-1, o0). Suppose that f: A R is a differentiable function with the properties %3D f(0) = 0, f'(x) %3D V1 + x3 a) Prove that f is injective. Let B f(A), and denote by g: B → R be the inverse function, so %3D y = f(x) + x = g(y). b) Express the derivative g'(y) in terms of g(y). c) Express the second derivative g" (y) in terms of g(y). Let A = (-1, o0). Suppose that f: A R is a differentiable function with the properties %3D f(0) = 0, f'(x) %3D V1 + x3 a) Prove that f is injective. Let B f(A), and denote by g: B → R be the inverse function, so %3D y = f(x) + x = g(y). b) Express the derivative g'(y) in terms of g(y). c) Express the second derivative g" (y) in terms of g(y).