An inverse function is a function that reverses another function, so we have a function called:
[tex]p(x)[/tex]
Then, the inverse function will be as follows:
[tex]p^{-1}(x) [/tex]
Given that [tex]y = p(x)[/tex], we need to isolate x in terms of y:
[tex]y = x^{2} -9[/tex]
∴ [tex]y+9 = x^{2}[/tex]
So:
[tex]x=+\sqrt{y+9}[/tex] and [tex]x=-\sqrt{y+9}[/tex]
therefore, exchanging variables x and y:
[tex]y=+\sqrt{x+9}[/tex] and [tex]y=-\sqrt{x+9}[/tex]
[tex]p^{-1}(x)=+\sqrt{x+9}[/tex] and [tex]p^{-1}(x)=-\sqrt{x+9}[/tex]
Which are the figures shown below.
