a. Let g(x) = 2x + 3 and h(x) = x³. Consider the composite function f(x) = g(h(x)). Find f^-1 directly and then express it in terms of g^-1 and h^-1.

b. Let g(x) = x² + 1 and h(x) = √x. Consider the composite function f(x) = g(h(x)). Find f^-1 directly and then express it in terms of g^-1 and h^-1.

c. Explain why if g and h are one-to-one, the inverse of f(x) = g(h(x)) exists.