Use the derivative to determine whether the function is strictly monotonic on its entire domain and therefore has an inverse function.

Question

f(x) = cos [(3x)/2]

Answer 1

Find f'(x) and solve for f'(x)=0.

If f'(x) has one or more extrema, i.e. where f"(x)≠0, then the function is not monotonic, and an inverse is undefined on its entire domain.

For the case of f(x)=cos(x), there should be an infinite number of extrema.