### Home > APCALC > Chapter 8 > Lesson 8.3.2 > Problem8-117

8-117.

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 $f(g(x)) = x$ for inverse functions. In other words, $f$ and $g$ are inverse functions.

Inverse functions have reciprocal slopes at corresponding $(x, y)→(y, x)$ points.

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