Answer :
to find the inverse
replace f(x) with y
switch all x and y
solve for y
replace y with f⁻¹(x)
f(x)=x^2-9
y=x^2-9
x=y^2-9
x+9=y^2
sqrt both sides
[tex] \sqrt{x+9} [/tex]
replace
f⁻¹(x)=[tex] \sqrt{x+9} [/tex]
that is the inverse
replace f(x) with y
switch all x and y
solve for y
replace y with f⁻¹(x)
f(x)=x^2-9
y=x^2-9
x=y^2-9
x+9=y^2
sqrt both sides
[tex] \sqrt{x+9} [/tex]
replace
f⁻¹(x)=[tex] \sqrt{x+9} [/tex]
that is the inverse