Find the inverse of the function.
-$$f ( x ) = \sqrt { x - 8 } , x \geq 8$$
A) $f ^ { - 1 } ( x ) = x ^ { 2 } + 8 , x \geq 0$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 8 , x \geq 0$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } + 8 , \mathrm { x } \geq 0$
D) Not a one-to-one function

Question

Quizplus · Accepted Answer

To find the inverse, swap $x$ and $y$ and solve for $y$: $x = \sqrt{y - 8}$. Squaring both sides gives $x^2 = y - 8$, so $y = x^2 + 8$, with $x \geq 0$ because the original function is defined for $x \geq 8$.

Find the Inverse of the Function f(x)=x−8,x≥8f ( x ) = \sqrt { x - 8 } , x \geq 8f(x)=x−8​,x≥8

Find the Inverse of the Function $f ( x ) = \sqrt { x - 8 } , x \geq 8$