1. **Problem:** Find the inverse of the function $f(x) = 2x - 3$ and determine if the inverse is a function, one-to-one function, or neither. 2. **Formula and rules:** To find the inverse of a function, swap $x$ and $y$ in the equation $y = f(x)$ and solve for $y$. The inverse is a function if each $x$ in the domain corresponds to exactly one $y$ in the range. 3. **Step-by-step solution:** - Start with $y = 2x - 3$. - Swap $x$ and $y$: $x = 2y - 3$. - Solve for $y$: $$x + 3 = 2y$$ $$y = \frac{x + 3}{2}$$ - So, the inverse function is: $$f^{-1}(x) = \frac{x + 3}{2}$$ 4. **Check if inverse is a function:** Since $f^{-1}(x)$ is a linear function, it passes the vertical line test and is one-to-one. 5. **Conclusion:** The inverse of $f(x) = 2x - 3$ is $f^{-1}(x) = \frac{x + 3}{2}$, and it is a one-to-one function.