The problem asks to find the inverse of the function $f(x) = \log_3(x+2)$.

1. Problem Description

The problem asks to find the inverse of the function $f(x) = \log_3(x+2)$.

2. Solution Steps

To find the inverse of the function $f(x) = \log_3(x+2)$, we first replace $f(x)$ with $y$:

$y = \log_3(x+2)$.

Then, we switch $x$ and $y$:

$x = \log_3(y+2)$.

Next, we solve for $y$. We rewrite the equation in exponential form:

$3^x = y+2$.

Finally, we isolate $y$ by subtracting 2 from both sides:

$y = 3^x - 2$.

Therefore, the inverse function is $f^{-1}(x) = 3^x - 2$.

3. Final Answer

$f^{-1}(x) = 3^x - 2$