The function $f ( x ) = \sqrt { x ^ { 2 } - 9 }$ is one-to-one on the domain $x \leq - \sqrt { 9 }$. Find $f ^ { - 1 } ( x )$.
A) $\quad f ^ { - 1 } ( x ) = x ^ { 2 } + 9$
B) $f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } + 9 }$
C) $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt { x ^ { 2 } - 9 } }$
D) $\quad f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } + 9 }$
E) $\quad f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } - 9 }$

Question

Quizplus · Accepted Answer

The inverse function is found by solving $y = \sqrt{x^2 - 9}$ for $x$, which gives $x = -\sqrt{y^2 + 9}$ since the domain is $x \leq -3$.

The Function f(x)=x2−9f ( x ) = \sqrt { x ^ { 2 } - 9 }f(x)=x2−9​

The Function $f ( x ) = \sqrt { x ^ { 2 } - 9 }$