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

Question

Quizplus · Accepted Answer

To find the inverse of the function $f(x) = (x + 7)^3$, you solve for $x$ in terms of $y$, then swap $x$ and $y$. This gives $y = (x + 7)^3$, so $x = \sqrt[3]{y} - 7$. Replace $y$ with $x$ to get the inverse function: $f^{-1}(x) = \sqrt[3]{x} - 7$.

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 $f ( x ) = ( x + 7 ) ^ { 3 }$