Find the inverse of the function.
-$$f ( x ) = x ^ { 3 } + 7$$
A) Not a one-to-one function
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } } - 7$
C) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x - 7 }$
D) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 7 }$

Question

Quizplus · Accepted Answer

To find the inverse, swap $x$ and $y$ and solve for $y$. Starting with $y = x^3 + 7$, swapping gives $x = y^3 + 7$, and solving for $y$ gives $y = \sqrt[3]{x - 7}$, which matches choice C.

Find the Inverse of the Function f(x)=x3+7f ( x ) = x ^ { 3 } + 7f(x)=x3+7

Find the Inverse of the Function $f ( x ) = x ^ { 3 } + 7$