Posted by **Erica** on Monday, December 6, 2010 at 2:06am.

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]

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**MathMate**, Monday, December 6, 2010 at 8:01am
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.

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