Question

for the function $f(x) = sqrt3{x} - 10$, find $f^{-1}(x)$. answer $f^{-1}(x) = x^3 - 10$ $f^{-1}(x) = (x - 10)^3$ $f^{-1}(x) = sqrt3{x} + 10$ $f^{-1}(x) = (x + 10)^3$ submit answer

Explanation:

Step1: Replace \( f(x) \) with \( y \)

We start with the function \( f(x) = \sqrt[3]{x} - 10 \). Let \( y = \sqrt[3]{x} - 10 \).

Step2: Solve for \( x \) in terms of \( y \)

First, add 10 to both sides of the equation: \( y + 10 = \sqrt[3]{x} \). Then, cube both sides to eliminate the cube root: \( (y + 10)^3 = x \).

Step3: Replace \( x \) with \( f^{-1}(x) \) and \( y \) with \( x \)

We get \( f^{-1}(x) = (x + 10)^3 \).

Answer:

D. \( f^{-1}(x) = (x + 10)^3 \)