A one-to-one function is given. Write an expression for the inverse function.
-$$f ( x ) = \sqrt [ 3 ] { x + 7 }$$
A) $f ^ { - 1 } ( x ) = ( x + 7 ) ^ { 3 }$
B) $f ^ { - 1 } ( x ) = x ^ { 3 } - 7$
C) $f ^ { - 1 } ( x ) = x ^ { 3 } + 7$
D) $f ^ { - 1 } ( x ) = ( x - 7 ) ^ { 3 }$

Question

Quizplus · Accepted Answer

To find the inverse function, swap $x$ and $y$ and solve for $y$. Starting with $y = \sqrt[3]{x + 7}$, swapping gives $x = \sqrt[3]{y + 7}$. Cubing both sides yields $x^3 = y + 7$, so $y = x^3 - 7$, which matches choice B.

A One-To-One Function Is Given f(x)=x+73f ( x ) = \sqrt [ 3 ] { x + 7 }f(x)=3x+7​

A One-To-One Function Is Given $f ( x ) = \sqrt [ 3 ] { x + 7 }$