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

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



Answer :

To find the inverse of the equation [tex]\( y = x^2 - 36 \)[/tex], follow these steps:

1. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]: The inverse function means we want to solve for [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex]. To do this, we first swap [tex]\( y \)[/tex] and [tex]\( x \)[/tex]:

[tex]\[ x = y^2 - 36 \][/tex]

2. Solve for [tex]\( y \)[/tex]: To solve for [tex]\( y \)[/tex], isolate [tex]\( y \)[/tex] on one side of the equation:

[tex]\[ x = y^2 - 36 \][/tex]

Add 36 to both sides:

[tex]\[ x + 36 = y^2 \][/tex]

3. Take the square root: To solve for [tex]\( y \)[/tex], take the square root of both sides. Remember to include both the positive and negative roots because [tex]\( y \)[/tex] could be either positive or negative:

[tex]\[ y = \pm \sqrt{x + 36} \][/tex]

So the inverse function of [tex]\( y = x^2 - 36 \)[/tex] is:

[tex]\[ y = \pm \sqrt{x + 36} \][/tex]

Among the provided multiple choices, the correct option is:

[tex]\[ \boxed{2. \, y = \pm \sqrt{x + 36}} \][/tex]