The problem asks us to find the inverse of the function $f(x) = 2x + 3$.

1. Problem Description

The problem asks us to find the inverse of the function $f(x) = 2x + 3$.

2. Solution Steps

To find the inverse of a function, we can follow these steps:

1. Replace $f(x)$ with $y$.

2. Swap $x$ and $y$.

3. Solve for $y$.

4. Replace $y$ with $f^{-1}(x)$.

Step 1: Replace $f(x)$ with $y$.

$y = 2x + 3$

Step 2: Swap $x$ and $y$.

$x = 2y + 3$

Step 3: Solve for $y$.

$x - 3 = 2y$

$y = \frac{x - 3}{2}$

Step 4: Replace $y$ with $f^{-1}(x)$.

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

3. Final Answer

The inverse of the function $f(x) = 2x + 3$ is $f^{-1}(x) = \frac{x - 3}{2}$.