### Home > CALC > Chapter 8 > Lesson 8.3.2 > Problem 8-116

8-116.

Suppose *f*(*g*(*x*)) = *x*, such that *f* and *g *are differentiable. If *f*(1) = 3 and* f* ′(1) = 2, determine the value of* g*′(3). Homework Help ✎

Recall that *f*(*g*(*x*)) = *x* is the definition of inverse functions. In other words, you are being told that *f*(*x*) and *g*(*x*) are inverses.

Inverse functions have reciprocal slopes at corresponding (*x*, *y*)→(*y*, *x*) values.