### Home > CALC > Chapter 8 > Lesson 8.3.2 > Problem8-116

8-116.

Suppose $f(g(x)) = x$, such that $f$ and $g$ are differentiable. If $f(1) = 3$ and $f^\prime(1) = 2$, determine the value of $g^\prime(3)$.

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.
For example, if $f(x)$ has coordinate point $(2, 3) \text{ and }f'(2)=\frac{4}{5},\text{ then }g'(3)=\frac{5}{4}$