The one-to-one function \( f \) is defined below. \( f(x)=3-x^{3} \) Find \( f^{-1}(x) \), where \( f^{-1} \) is the inverse of \( f \). \( f^{-1}(x)=\square \)

To find the inverse of the function \( f(x) = 3 - x^3 \), we start by letting \( y = f(x) \). Thus, we have: \[ y = 3 - x^3 \] Next, we solve for \( x \) in terms of \( y \): 1. Rearrange the equation: \( x^3 = 3 - y \) 2. Take the cube root of both sides: \( x = \sqrt[3]{3 - y} \) Now, we express the inverse function by swapping \( x \) and \( y \): \[ f^{-1}(x) = \sqrt[3]{3 - x} \] Thus, the final answer is: \[ f^{-1}(x) = \sqrt[3]{3 - x} \]