Find the inverse of the function.
-$f ( x ) = - x ^ { 2 } + 12 , x \geq 0$
A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { 12 - \mathrm { x } }$
B) $f ^ { - 1 } ( x ) = x ^ { 2 } + 12$
C) $f ^ { - 1 } ( x ) = \sqrt { x + 12 }$
D) $f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } + 12 }$

Question

Quizplus · Accepted Answer

To find the inverse, swap $x$ and $y$ and solve for $y$. Starting with $y = -x^2 + 12$, swap to get $x = -y^2 + 12$, then solve for $y$ to get $y = \sqrt{12 - x}$, considering $x \geq 0$.

Find the Inverse of the Function f(x)=−x2+12,x≥0f ( x ) = - x ^ { 2 } + 12 , x \geq 0f(x)=−x2+12,x≥0

Find the Inverse of the Function $f ( x ) = - x ^ { 2 } + 12 , x \geq 0$