Question

If the slope of a strictly increasing function at the point (a, b) is 6, what is the slope of the inverse of the function at the point (b, a)?

Answer 1

$$\left[f^{-1}\right]'(b) = \frac{1}{f'(f^{-1}(b))} = \frac{1}{f'(a)} = \frac{1}{6}$$

Answer 2

It should be noted that the inverse exists since the function is strictly increasing (and therefore one to one).