Which equation is the inverse of [tex]$y = x^2 + 16$[/tex]?

A. [tex]$y = x^2 - 16$[/tex]
B. [tex]$y = \pm \sqrt{x} - 16$[/tex]
C. [tex][tex]$y = \pm \sqrt{x - 16}$[/tex][/tex]
D. [tex]$y = x^2 - 4$[/tex]



Answer :

To find the inverse of the function [tex]\( y = x^2 + 16 \)[/tex], we need to express [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex].

1. Start with the given function:
[tex]\[ y = x^2 + 16 \][/tex]

2. To find the inverse, switch the roles of [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[ x = y^2 + 16 \][/tex]

3. Solve this equation for [tex]\( y \)[/tex]:

[tex]\[ x - 16 = y^2 \][/tex]

4. Isolate [tex]\( y \)[/tex] by taking the square root of both sides. Remember, taking the square root of both sides introduces a [tex]\(\pm\)[/tex] (plus-minus) sign:
[tex]\[ y = \pm \sqrt{x - 16} \][/tex]

Thus, the inverse function is:
[tex]\[ y = \pm \sqrt{x - 16} \][/tex]

Therefore, the correct option corresponding to the inverse function [tex]\( y = \pm \sqrt{x - 16} \)[/tex] is the third option:

[tex]\[ \boxed{y = \pm \sqrt{x - 16}} \][/tex]