Find the inverse of the function.
-$$f ( x ) = \sqrt { x } - 5 , x \geq 0$$
A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } + 5 , \mathrm { x } \geq 5$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - ( \mathrm { x } + 5 ) ^ { 2 } , \mathrm { x } \geq 5$
C) $f ^ { - 1 } ( x ) = ( x - 5 ) ^ { 2 }$
D) $f ^ { - 1 } ( x ) = ( x + 5 ) ^ { 2 } , x \geq 5$

Question

Quizplus · Accepted Answer

To find the inverse of the function, we switch the x and y variables and solve for y.

$$x = \sqrt { y } - 5$$
$$x + 5 = \sqrt { y }$$
$$(x + 5)^2 = y$$

So the inverse function is: 
$$f ^ { - 1 } ( x ) = ( x + 5 ) ^ { 2 } , x \geq 0$$
Note that we need to specify that x is greater than or equal to 0, since the original function is only valid for x greater than or equal to 0. Therefore, choice D is the correct answer.

Find the Inverse of the Function f(x)=x−5,x≥0f ( x ) = \sqrt { x } - 5 , x \geq 0f(x)=x​−5,x≥0

Find the Inverse of the Function $f ( x ) = \sqrt { x } - 5 , x \geq 0$