Find the inverse of the function. $g ( x ) = x ^ { 2 } - 16 , x \geq 0$
A) $g ^ { - 1 } ( x ) = - \sqrt { x + 16 }$
B) $g ^ { - 1 } ( x ) = \sqrt { x + 16 }$
C) $g ^ { - 1 } ( x ) = 4 + \sqrt { x }$
D) $g ^ { - 1 } ( x ) = 4 - \sqrt { x }$
E) none of these

Question

Quizplus · Accepted Answer

To find the inverse of the function, we can start by replacing g(x) with y and solve for x.
y = x^2 - 16
y + 16 = x^2
x = sqrt(y + 16) (because x≥0)
Therefore, the inverse function is g^-1(x) = sqrt(x + 16). Choice B is the correct answer.

Find the Inverse of the Function g(x)=x2−16,x≥0g ( x ) = x ^ { 2 } - 16 , x \geq 0g(x)=x2−16,x≥0

Find the Inverse of the Function $g ( x ) = x ^ { 2 } - 16 , x \geq 0$