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

Question

Quizplus · Accepted Answer

To find the inverse of $f(x) = x^3 + 1$, you swap $x$ and $y$ and solve for $y$. So, $x = y^3 + 1$. Solving for $y$ gives $y = \sqrt[3]{x - 1}$, which corresponds to choice A.

The Function F Is One-To-One f(x)=x3+1f ( x ) = x ^ { 3 } + 1f(x)=x3+1

The Function F Is One-To-One $f ( x ) = x ^ { 3 } + 1$