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

Question

Quizplus · Accepted Answer

To find the inverse function, you swap $x$ and $y$ and solve for $y$. Starting with $y = r(x + q)^7 + s$, swapping $x$ and $y$ gives $x = r(y + q)^7 + s$. Solving for $y$ involves subtracting $s$, dividing by $r$, and taking the seventh root, leading to $y = \sqrt[7]{\frac{x - s}{r}} - q$, which matches option C.

A One-To-One Function Is Given g(x)=r(x+q)7+sg ( x ) = r ( x + q ) ^ { 7 } + sg(x)=r(x+q)7+s

A One-To-One Function Is Given $g ( x ) = r ( x + q ) ^ { 7 } + s$