Please solve the following (see image)

Characterizing a Function of a Random Variable Let X be a continuous random variable with probability density function f(x), and let h be an invertible function where his differentiable. Recall that Y = h(X ) is itself a continuous random variable. (Bonus + 3 points) Prove that the probability density function of Y is g(y) = f(h-'(y)) . d dy h-' (y)