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

Question

Quizplus · Accepted Answer

To find the inverse of the function $f(x) = (x + 2)^3 - 1$, we replace $f(x)$ with $y$, and then solve for $x$ in terms of $y$:$$y = (x + 2)^3 - 1$$$$y + 1 = (x + 2)^3$$$$x + 2 = \sqrt[3]{y + 1}$$$$x = \sqrt[3]{y + 1} - 2$$Then, we replace $x$ with $f^{-1}(x)$ and $y$ with $x$ to get the inverse function:$$f^{-1}(x) = \sqrt[3]{x + 1} - 2$$

Find the Inverse of the One-To-One Function f(x)=(x+2)3−1f ( x ) = ( x + 2 ) ^ { 3 } - 1f(x)=(x+2)3−1

Find the Inverse of the One-To-One Function $f ( x ) = ( x + 2 ) ^ { 3 } - 1$