Problem

Given the function \(f(x) = 2x + 3\), find the inverse function \(f^{-1}(x)\).

Answer

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Answer

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

Steps

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

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