The function f is one-to-one. Find its inverse.
-$$f ( x ) = \sqrt [ 3 ] { x + 5 }$$
A) $f ^ { - 1 } ( x ) = x ^ { 3 } - 5$
B) $f ^ { - 1 } ( x ) = \frac { 1 } { x ^ { 3 } - 5 }$
C) $f ^ { - 1 } ( x ) = x ^ { 3 } + 25$
D) $f ^ { - 1 } ( x ) = x - 5$

Question

Quizplus · Accepted Answer

To find the inverse of $f(x) = \sqrt[3]{x + 5}$, you swap $x$ and $y$ and solve for $y$. So, $x = \sqrt[3]{y + 5}$ becomes $x^3 = y + 5$, which simplifies to $y = x^3 - 5$. Therefore, $f^{-1}(x) = x^3 - 5$.

The Function F Is One-To-One f(x)=x+53f ( x ) = \sqrt [ 3 ] { x + 5 }f(x)=3x+5​

The Function F Is One-To-One $f ( x ) = \sqrt [ 3 ] { x + 5 }$