Find the inverse of the one-to-one function.
-$f ( x ) = x ^ { 3 } + 8$
A) $f ^ { - 1 } ( x ) = - x ^ { 3 } - 8$
B) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 8 }$
C) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 8 }$
D) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } - 8$

Question

Quizplus · Accepted Answer

To find the inverse function, swap $x$ and $y$ and solve for $y$. Starting with $y = x^3 + 8$, swapping gives $x = y^3 + 8$, and solving for $y$ gives $y = \sqrt[3]{x - 8}$, which matches choice B.

Find the Inverse of the One-To-One Function f(x)=x3+8f ( x ) = x ^ { 3 } + 8f(x)=x3+8

Find the Inverse of the One-To-One Function $f ( x ) = x ^ { 3 } + 8$