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# Conditions Required for a Differentiable Inverse

APCALC-49VFM9

Suppose that $f(x)$ is a function that is defined for all real numbers.

Which of the following conditions would assure that $f(x)$ has a differentiable inverse?

I. $f'(x) \gt 0$ for all values of $x$
II. $f(x)$ is a strictly decreasing function
III. $f(x)$ is an odd function

A

I only

B

I and II only

C

I, II and III

D

None of them are sufficient