Find the inverse of the function.
-$$f ( x ) = \sqrt [ 3 ] { \frac { x } { 9 } } - 8$$
A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 27 ( \mathrm { x } + 8 )$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 9 ( \mathrm { x } + 8 ) ^ { 3 }$
C) $f ^ { - 1 } ( x ) = 9 \left( x ^ { 3 } + 8 \right)$
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = [ 9 ( \mathrm { x } + 8 ) ] ^ { 3 }$

Question

Quizplus · Accepted Answer

To find the inverse, swap $x$ and $y$ and solve for $y$. Starting with $y = \sqrt[3]{\frac{x}{9}} - 8$, swap to get $x = \sqrt[3]{\frac{y}{9}} - 8$. Solve for $y$ by isolating the cube root, then cube both sides and solve for $y$, resulting in $y = 9(x + 8)^3$.

Find the Inverse of the Function f(x)=x93−8f ( x ) = \sqrt [ 3 ] { \frac { x } { 9 } } - 8f(x)=39x​​−8

Find the Inverse of the Function $f ( x ) = \sqrt [ 3 ] { \frac { x } { 9 } } - 8$