Question

question
for the function $f(x) = (x - 9)^{\frac{1}{3}}$, find $f^{-1}(x)$.
answer attempt 1 out of 2
$\circ$ $f^{-1}(x) = (x + 9)^3$ $\circ$ $f^{-1}(x) = (x - 9)^3$
$\circ$ $f^{-1}(x) = x^3 - 9$ $\circ$ $f^{-1}(x) = x^3 + 9$

Explanation:

Step1: Set $y = f(x)$

$y = (x - 9)^{\frac{1}{3}}$

Step2: Swap $x$ and $y$

$x = (y - 9)^{\frac{1}{3}}$

Step3: Cube both sides

$x^3 = y - 9$

Step4: Solve for $y$

$y = x^3 + 9$

Answer:

$f^{-1}(x) = x^3 + 9$