1. **State the problem:** Find the value of the inverse function $f^{-1}(3)$ given $f(x) = 2x - 1$. 2. **Recall the formula for inverse functions:** To find $f^{-1}(y)$, solve the equation $y = f(x)$ for $x$. 3. **Set up the equation:** Let $y = 3$, so we have $$3 = 2x - 1$$ 4. **Solve for $x$:** Add 1 to both sides: $$3 + 1 = 2x$$ $$4 = 2x$$ Divide both sides by 2: $$\frac{4}{\cancel{2}} = x \cancel{\frac{1}{2}}$$ $$x = 2$$ 5. **Interpretation:** The inverse function value $f^{-1}(3) = 2$ means that when $x=2$, $f(x)=3$. **Final answer:** $$f^{-1}(3) = 2$$