The problem asks to find the inverse function $f^{-1}(y)$ of the given function $f(x) = 2(x+2) + 5$.

1. Problem Description

The problem asks to find the inverse function $f^{-1}(y)$ of the given function $f(x) = 2(x+2) + 5$.

2. Solution Steps

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

$y = 2(x+2) + 5$

Next, we solve for $x$ in terms of $y$.

$y = 2(x+2) + 5$

$y = 2x + 4 + 5$

$y = 2x + 9$

$y - 9 = 2x$

$x = \frac{y - 9}{2}$

Finally, we replace $x$ with $f^{-1}(y)$.

$f^{-1}(y) = \frac{y - 9}{2}$

3. Final Answer

$f^{-1}(y) = \frac{y - 9}{2}$