Which equation is the inverse of [tex]\( y = x^2 - 36 \)[/tex]?

A. [tex]\( y = \pm \sqrt{x} + 6 \)[/tex]
B. [tex]\( y = \pm \sqrt{x + 36} \)[/tex]
C. [tex]\( y = \pm \sqrt{x} + 36 \)[/tex]
D. [tex]\( y = \pm \sqrt{x^2 + 36} \)[/tex]



Answer :

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]