Let f and g be differentiable functions on R such that f g is the identity function.

Question

Let $f$ and $g$ be differentiable functions on $\mathbb{R}$ such that $f\circ g$ is the identity function. If for some $a,b\in\mathbb{R}$, $g'(a)=5$ and $g(a)=b$, then $f'(b)$ is equal to:

Accepted Answer

$f(g(x))=x\Rightarrow f'(g(x))g'(x)=1$. At $x=a$: $f'(b)\cdot5=1\Rightarrow f'(b)=\dfrac15$.

Solutions · 1