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Find the inverse function of \( f(x)=4+\sqrt[3]{x} \) \( f^{-1}(x)=\square \)

Ask by Schofield Warner. in the United States
Mar 15,2025

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The inverse function is \( f^{-1}(x) = (x - 4)^3 \).

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To find the inverse of the function \( f(x) = 4 + \sqrt[3]{x} \), we start by replacing \( f(x) \) with \( y \): \[ y = 4 + \sqrt[3]{x} \] Next, we solve for \( x \) in terms of \( y \): 1. Subtract 4 from both sides: \[ y - 4 = \sqrt[3]{x} \] 2. Now, cube both sides to eliminate the cube root: \[ (y - 4)^3 = x \] Now, we have expressed \( x \) in terms of \( y \). To write the inverse function, we swap \( x \) and \( y \): \[ f^{-1}(x) = (x - 4)^3 \] Thus, the inverse function is: \[ f^{-1}(x) = (x - 4)^3 \]

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