To find the inverse of the equation [tex]\( y = x^2 - 36 \)[/tex], we follow the steps below:
1. Start with the original equation:
[tex]\[
y = x^2 - 36
\][/tex]
2. Swap [tex]\(x\)[/tex] and [tex]\(y\)[/tex]:
This step helps us find the inverse function. So we swap [tex]\(x\)[/tex] and [tex]\(y\)[/tex] in the equation:
[tex]\[
x = y^2 - 36
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
We need to solve this equation for [tex]\(y\)[/tex]. First, isolate [tex]\(y^2\)[/tex] on one side of the equation:
[tex]\[
y^2 = x + 36
\][/tex]
4. Take the square root of both sides:
When we take the square root of both sides, we need to remember to include both the positive and negative solutions:
[tex]\[
y = \pm \sqrt{x + 36}
\][/tex]
So, the inverse of the equation [tex]\( y = x^2 - 36 \)[/tex] is:
[tex]\[
y = \pm \sqrt{x + 36}
\][/tex]
Among the given options, the correct one is:
[tex]\[
y = \pm \sqrt{x + 36}
\][/tex]
