Find the inverse of the one-to-one function.
-$$f ( x ) = x ^ { 3 } + 2$$
A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } + 2 }$
B) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 2 }$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } } - 2$
D) $f ^ { - 1 } ( x ) = - x ^ { 3 } - 2$

Question

Quizplus · Accepted Answer

To find the inverse function, swap $x$ and $y$ and solve for $y$. Starting with $y = x^3 + 2$, swapping gives $x = y^3 + 2$. Solving for $y$ gives $y = \sqrt[3]{x - 2}$, which matches choice B.

Find the Inverse of the One-To-One Function f(x)=x3+2f ( x ) = x ^ { 3 } + 2f(x)=x3+2

Find the Inverse of the One-To-One Function $f ( x ) = x ^ { 3 } + 2$