Use the derivative to determine whether the function is strictly monotonic on its entire domain and therefore has an inverse function.
f(x) = cos [(3x)/2]
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.posted by MathMate