Find the inverse of the one-to-one function.
-$$f ( x ) = ( x - 4 ) ^ { 3 }$$
A) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } + 4$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } } - 4$
C) $f ^ { - 1 } ( x ) = \sqrt { x } + 4$
D) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } + 64$

Question

Quizplus · Accepted Answer

To find the inverse of $f(x) = (x - 4)^3$, you swap $x$ and $y$ and solve for $y$. This gives $x = (y - 4)^3$, and solving for $y$ gives $y = \sqrt[3]{x} + 4$, which matches choice A.

Find the Inverse of the One-To-One Function f(x)=(x−4)3f ( x ) = ( x - 4 ) ^ { 3 }f(x)=(x−4)3

Find the Inverse of the One-To-One Function $f ( x ) = ( x - 4 ) ^ { 3 }$