Please show all the steps and what theorems you used.

Suppose f(r) is an increasing, invertible and concave up function for all r e R. Let h denote the inverse function of f and suppose the second derivative of h satisfies /"(x) = - f*(h(x)) (f(h(x)))3 Prove the inverse function of f is concave down for all c E R. As part of your solution, state the theorems (if any) used in your proof