1. The problem asks us to find the inverse function $g^{-1}(x)$ of the given function $g(x) = \frac{x - 10}{8}$.\n\n2. To find the inverse, we start by replacing $g(x)$ with $y$: $$y = \frac{x - 10}{8}$$\n\n3. The inverse function swaps $x$ and $y$, so we write: $$x = \frac{y - 10}{8}$$\n\n4. Now solve for $y$: multiply both sides by 8 to eliminate the denominator: $$8x = y - 10$$\n\n5. Add 10 to both sides to isolate $y$: $$y = 8x + 10$$\n\n6. Therefore, the inverse function is: $$g^{-1}(x) = 8x + 10$$\n\nThis expression is expanded and simplified as requested.