If [tex]f^{-1}(x)[/tex] is the inverse of [tex]f(x)[/tex], then by definition
[tex]f\left(f^{-1}(x)\right) = x[/tex]
Given that [tex]f(x)=9x+7[/tex], we have
[tex]f\left(f^{-1}(x)\right) = 9f^{-1}(x)+7 = x[/tex]
Solve for [tex]f^{-1}(x)[/tex] :
[tex]9f^{-1}(x) + 7 = x \\\\ 9f^{-1}(x) = x - 7 \\\\ f^{-1}(x) = \dfrac{x-7}9[/tex]
