To find the inverse of a function, replace every x in the equation with a y, and replace every y in the equation with an x:
[tex]x = y^{2} - 9[/tex]
Add 9 to both sides:
[tex]y^{2} = x + 9[/tex]
Square root both sides to get y by itself:
[tex]y = \sqrt{x+9}[/tex]
This equation can be simplified by taking the square root of 9 out of the root:
[tex]\sqrt{9} = 3[/tex]
[tex]y = 3 + \sqrt{x}[/tex]
The inverse of this function is y = 3 + √x.
