To determine the inverse of the function [tex]\( y = 100 - x^2 \)[/tex], we need to follow these steps:
1. Start with the original function:
[tex]\[ y = 100 - x^2 \][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to find the inverse function:
[tex]\[ x = 100 - y^2 \][/tex]
3. Solve for [tex]\( y \)[/tex]:
[tex]\[
x = 100 - y^2
\][/tex]
[tex]\[
y^2 = 100 - x
\][/tex]
4. Take the square root of both sides to solve for [tex]\( y \)[/tex]:
[tex]\[
y = \pm \sqrt{100 - x}
\][/tex]
Thus, the equation for the inverse of [tex]\( y = 100 - x^2 \)[/tex] is:
[tex]\[ y = \pm \sqrt{100 - x} \][/tex]
Therefore, the correct answer is:
[tex]\[ y = \pm \sqrt{100 - x} \][/tex]
