The function f is one-to-one. Find its inverse.
-$$f ( x ) = ( x + 2 ) ^ { 3 } - 8$$
A) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 6 }$
B) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 2 } + 8$
C) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 10 }$
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } + 8 } - 2$

Question

Quizplus · Accepted Answer

To find the inverse function, swap $x$ and $y$ and solve for $y$. Starting with $y = (x + 2)^3 - 8$, swap to get $x = (y + 2)^3 - 8$, then solve for $y$: $x + 8 = (y + 2)^3$, leading to $y = \sqrt[3]{x + 8} - 2$.

The Function F Is One-To-One f(x)=(x+2)3−8f ( x ) = ( x + 2 ) ^ { 3 } - 8f(x)=(x+2)3−8

The Function F Is One-To-One $f ( x ) = ( x + 2 ) ^ { 3 } - 8$