Find the inverse of the function.
-$$f ( x ) = \sqrt { x + 3 } , x \geq - 3$$
A) $f ^ { - 1 } ( x ) = - x ^ { 2 } + 3 , x \geq 0$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 9 , \mathrm { x } \geq 0$
C) $f ^ { - 1 } ( x ) = x ^ { 2 } - 3 , x \geq 0$
D) Not a one-to-one function

Question

Quizplus · Accepted Answer

To find the inverse of a function, switch the $x$ and $y$ variables and solve for $y$. 
Starting with $f(x) = \sqrt{x+3}$:
$$y = \sqrt{x+3}$$
$$x = \sqrt{y+3}$$
$$x^2 = y+3$$
$$y = x^2 - 3 \quad 	ext{(Note that } x \geq 0 	ext{ since }\sqrt{y+3} \geq 0 	ext{)}$$
Therefore, the inverse function is $f^{-1}(x) = x^2-3$, $x\geq 0$.

Find the Inverse of the Function f(x)=x+3,x≥−3f ( x ) = \sqrt { x + 3 } , x \geq - 3f(x)=x+3​,x≥−3

Find the Inverse of the Function $f ( x ) = \sqrt { x + 3 } , x \geq - 3$