Solve the problem.
-$$f ( x ) = \sqrt { x - 5 } + 7$$
A) $f ^ { - 1 } ( x ) = ( x + 5 ) ^ { 2 } - 7 , x \geq - 5$
B) $f ^ { - 1 } ( x ) = x ^ { 2 } + 7 , x \geq 0$
C) $f ^ { - 1 } ( x ) = ( x - 7 ) ^ { 2 } + 5 , x \geq 7$
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = ( \mathrm { x } + 7 ) ^ { 2 } - 5 , \mathrm { x } \geq - 7$

Question

Quizplus · Accepted Answer

To find the inverse of a function, we interchange the roles of x and y and then solve for y. So we have:
$$y = \sqrt{x-5} + 7$$
Interchanging x and y:
$$x = \sqrt{y-5} + 7$$
Solving for y:
$$y = (x-7)^2 + 5$$
Therefore, the inverse function is:
$$f^{-1}(x) = (x-7)^2 + 5,\ x\geq7$$
Option C is the only choice that matches this.

Solve the Problem f(x)=x−5+7f ( x ) = \sqrt { x - 5 } + 7f(x)=x−5​+7

Solve the Problem $f ( x ) = \sqrt { x - 5 } + 7$