2. Let f(x) = x³ – 8, and let g be the inverse function of f. For what value in the domain of g is g not differentiable?

First find the inverse function of f by the following three steps:

Step 1: Write y = f(x).

Step 2: Solve for x in terms of y.

Step 3: Interchange x and y. The resulting equation is the inverse function g in terms of x.

Differentiate g(x) to find the value in the domain of g where g is not differentiable. In other words, where is g’(x) not defined.

Clearly, g is not differentiable at x = -8.