Find the inverse of the one-to-one function.
-$$f ( x ) = \sqrt { x - 6 }$$
A) $f ^ { - 1 } ( x ) = x ^ { 2 } + 6$
B) $f ^ { - 1 } ( x ) = \frac { 1 } { x ^ { 2 } + 6 }$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } + 6$
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 6$

Question

Quizplus · Accepted Answer

To find the inverse function, swap $x$ and $y$ and solve for $y$. Starting with $y = \sqrt{x - 6}$, swapping gives $x = \sqrt{y - 6}$. Squaring both sides yields $x^2 = y - 6$, and solving for $y$ gives $y = x^2 + 6$, which matches choice A.

Find the Inverse of the One-To-One Function f(x)=x−6f ( x ) = \sqrt { x - 6 }f(x)=x−6​

Find the Inverse of the One-To-One Function $f ( x ) = \sqrt { x - 6 }$