Chapter 6 - Logarithmic Functions - 6.1 Functions and Their Inverses - 6.1 Exercises - Page 494: 39

$h^{-1}(x) = \frac{3x+27}{2}$

$h(x) = \frac{2}{3}x -9$ Let $h(x) = y$: $y = \frac{2}{3}x - 9$ Switch the variables $x$ and $y$ to find the inverse and solve for $y$: $x = \frac{2}{3}y -9 $ $x + 9 = \frac{2}{3}y$ $x + 9 = \frac{2y}{3}$ $3x + 27 = 2y$ $y = \frac{3x+27}{2}$ $h^{-1}(x) = \frac{3x+27}{2}$