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Which equation is the inverse of [tex]\( y = 100 - x^2 \)[/tex]?

A. [tex]\( y = \pm \sqrt{100 - x} \)[/tex]
B. [tex]\( y = 10 \pm \sqrt{x} \)[/tex]
C. [tex]\( y = 100 \pm \sqrt{x} \)[/tex]
D. [tex]\( y = \pm \sqrt{x - 100} \)[/tex]

Sagot :

GinnyAnswer
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]
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