1. **Problem:** Find the inverse of the function $f(x) = 2x - 3$ and state if the inverse is a function, one-to-one function, or neither. 2. **Formula and rules:** To find the inverse function $f^{-1}(x)$, swap $x$ and $y$ in the equation $y = f(x)$ and solve for $y$. A function is one-to-one if each $x$ corresponds to exactly one $y$ and vice versa, which ensures the inverse is also a function. 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 $f(x) = 2x - 3$ is a linear function with a non-zero slope, it is one-to-one. Therefore, its inverse $f^{-1}(x) = \frac{x + 3}{2}$ is also a function and one-to-one. **Final answer:** $$f^{-1}(x) = \frac{x + 3}{2}$$, which is a one-to-one function.