Answer :
To make this simpler, make f(x) be y.
[tex]f(x)= x^{2} -81\\ y=x^{2} -81\\[/tex]
Switch x and y to find inverse
[tex]y=x^{2} -81\\ x=y^{2} -81\\[/tex]
Now, solve for y.
[tex]x=y^{2} -81\\ x+81=y^{2} -81+81\\ x+81=y^{2}\\ \sqrt{x+81} = \sqrt{y^{2}} \\ y =\sqrt{x+81}[/tex]
[tex]f(x)= x^{2} -81\\ y=x^{2} -81\\[/tex]
Switch x and y to find inverse
[tex]y=x^{2} -81\\ x=y^{2} -81\\[/tex]
Now, solve for y.
[tex]x=y^{2} -81\\ x+81=y^{2} -81+81\\ x+81=y^{2}\\ \sqrt{x+81} = \sqrt{y^{2}} \\ y =\sqrt{x+81}[/tex]
