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

Question

Quizplus · Accepted Answer

To find the inverse function, swap $x$ and $y$ and solve for $y$. Starting with $y = x^3 + 4$, we swap to get $x = y^3 + 4$, and solving for $y$ gives $y = \sqrt[3]{x - 4}$, which matches choice A.

The Function F Is One-To-One f(x)=x3+4f ( x ) = x ^ { 3 } + 4f(x)=x3+4

The Function F Is One-To-One $f ( x ) = x ^ { 3 } + 4$