Problem

Find the inverse of the function \( f(x) = 3x - 7 \).

Answer

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Answer

Step 4: Replace \( y \) with \( f^{-1}(x) \) to get the inverse function: \( f^{-1}(x) = \frac{x+7}{3} \).

Steps

Step 1 ：Step 1: Replace \( f(x) \) with \( y \), so the equation becomes \( y = 3x - 7 \).

Step 2 ：Step 2: Swap \( x \) and \( y \) to get \( x = 3y - 7 \).

Step 3 ：Step 3: Solve the equation for \( y \) to get \( y = \frac{x+7}{3} \).

Step 4 ：Step 4: Replace \( y \) with \( f^{-1}(x) \) to get the inverse function: \( f^{-1}(x) = \frac{x+7}{3} \).

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