3.36: Sec function range, gf and inverse sketch

The function $f$ is defined by $f(x) = \mathrm{sec}\,x$ for $\dfrac{2\pi}{3} \leqslant x \leqslant \pi$. Find the range of $f$.

Solve $f(x) = -\dfrac{2}{\sqrt{3}}$.

Given $g(x) = 3 - x^{2}$ for all real $x$ and that $gf$ exists, state the domain of $gf$.

Solve $gf(x) = 1$.

The function $h$ is defined by $h(x) = \ln(x - 4)$ for $x > 4$. Sketch $y = h(x)$ and $y = h^{-1}(x)$, showing asymptotes and axis intercepts.