Find the inverse of the function. $$g ( x ) = x ^ { 2 } - 9 , x \geq 0$$
A) $g ^ { - 1 } ( x ) = - \sqrt { x + 9 }$
B) $g ^ { - 1 } ( x ) = \sqrt { x + 9 }$
C) $g ^ { - 1 } ( x ) = 9 + \sqrt { x }$
D) $g ^ { - 1 } ( x ) = 9 - \sqrt { x }$
E) none of these

Question

Quizplus · Accepted Answer

To find the inverse we need to swap the roles of x and y and then solve for y.

So, let: 
            x = y^2 - 9 
Adding 9 to both sides, we get 
            x + 9 = y^2 
Taking the square root of both sides, we get 
            y = sqrt(x+9), where y >= 0 since given that x >= 0. 
Therefore, the inverse is: 
            g^-1(x) = sqrt(x+9), which is given by choice (B).

Find the Inverse of the Function g(x)=x2−9,x≥0g ( x ) = x ^ { 2 } - 9 , x \geq 0g(x)=x2−9,x≥0

Find the Inverse of the Function $g ( x ) = x ^ { 2 } - 9 , x \geq 0$