Problem
Given the function \(f(x) = 2x + 3\), find the inverse function \(f^{-1}(x)\).
Solution
Step 1 ：To find the inverse function, we first replace the function notation \(f(x)\) with \(y\). So we have \(y = 2x + 3\).
Step 2 ：Next we swap \(x\) and \(y\). This gives us \(x = 2y + 3\).
Step 3 ：Finally, we solve for \(y\) to get the inverse function. Subtract 3 from both sides to get \(x - 3 = 2y\), then divide by 2 to get \(y = \frac{x - 3}{2}\). This is the inverse function, so we can write \(f^{-1}(x) = \frac{x - 3}{2}\).
