The function f is one-to-one. Find its inverse.
-$$f ( x ) = ( x + 7 ) ^ { 3 }$$
A) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } + 7$
B) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } - 343$
C) $f ^ { - 1 } ( x ) = \sqrt { x } - 7$
D) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x } - 7$

Question

Quizplus · Accepted Answer

To find the inverse function, swap $x$ and $y$ and solve for $y$. Starting with $y = (x + 7)^3$, swapping gives $x = (y + 7)^3$. Solving for $y$ gives $y = \sqrt[3]{x} - 7$, which matches option D.

The Function F Is One-To-One f(x)=(x+7)3f ( x ) = ( x + 7 ) ^ { 3 }f(x)=(x+7)3

The Function F Is One-To-One $f ( x ) = ( x + 7 ) ^ { 3 }$