Chapter 7 - Analytic Trigonometry - 7.2 The Inverse Trigonometric Functions (Continued) - 7.2 Assess Your Understanding - Page 458: 72

$-\frac{3}{4}$

Step 1. Letting $g^{-1}(-\frac{4}{5})=cos^{-1}(-\frac{4}{5})=t$, we have $cos(t)=-\frac{4}{5}$ and $t$ in quadrant II. Step 2. Form a right triangle with sides $x=4, r=5, y=\sqrt {r^2-x^2}=3$ with $\pi-|t|$ facing $y$. Step 3. We have $h(g^{-1}(-\frac{4}{5}))=tan(t)=-\frac{3}{4}$