Write an equation of the inverse for the one-to-one function $$g ( x ) = x ^ { 2 } + 4 \text { where } x \geq 0$$
A) $g ^ { - 1 } ( x ) = \sqrt { x } - 2$
B) $g ^ { - 1 } ( x ) = \sqrt { x - 4 }$
C) $g ^ { - 1 } ( x ) = g ^ { - 1 } ( x ) = \sqrt { x + 4 }$
D) $g ^ { - 1 } ( x ) = \sqrt { x } + 2$

Question

Write an equation of the inverse for the one-to-one function $$g ( x ) = x ^ { 2 } + 4 \text { where } x \geq 0$$ 
A) $g ^ { - 1 } ( x ) = \sqrt { x } - 2$
B) $g ^ { - 1 } ( x ) = \sqrt { x - 4 }$
C) $g ^ { - 1 } ( x ) = g ^ { - 1 } ( x ) = \sqrt { x + 4 }$
D) $g ^ { - 1 } ( x ) = \sqrt { x } + 2$

Quizplus · Accepted Answer

To find the inverse function, swap $x$ and $y$ in the original equation and solve for $y$. Starting with $y = x^2 + 4$, swapping gives $x = y^2 + 4$. Solving for $y$ gives $y = \sqrt{x - 4}$, which matches choice B.

Write an Equation of the Inverse for the One-To-One Function g(x)=x2+4 where x≥0g ( x ) = x ^ { 2 } + 4 \text { where } x \geq 0g(x)=x2+4 where x≥0

Write an Equation of the Inverse for the One-To-One Function $g ( x ) = x ^ { 2 } + 4 \text { where } x \geq 0$