The problem asks us to find the inverse function $f^{-1}(y)$ given the function $f(x) = 8(x-2) + 4$.

1. Problem Description

The problem asks us to find the inverse function $f^{-1}(y)$ given the function $f(x) = 8(x-2) + 4$.

2. Solution Steps

To find the inverse function $f^{-1}(y)$, we first replace $f(x)$ with $y$, so we have:

$y = 8(x-2) + 4$

Now we solve for $x$ in terms of $y$:

$y = 8x - 16 + 4$

$y = 8x - 12$

$y + 12 = 8x$

$x = \frac{y + 12}{8}$

Now we replace $x$ with $f^{-1}(y)$:

$f^{-1}(y) = \frac{y + 12}{8}$

3. Final Answer

$f^{-1}(y) = \frac{y+12}{8}$