Answer:
[tex]\large\boxed{f^{-1}(x)=9x-18}[/tex]
Step-by-step explanation:
[tex]f(x)=\dfrac{1}{9}x+2\to y=\dfrac{1}{9}x+2\\\\\text{exchange x to y and vice versa}\\\\x=\dfrac{1}{9}y+2\\\\\text{solve for y}\\\\\dfrac{1}{9}y+2=x\qquad\text{subtract 2 from both sides}\\\\\dfrac{1}{9}y=x-2\qquad\text{multiply both sides by 9}\\\\9\!\!\!\!\diagup^1\cdot\dfrac{1}{9\!\!\!\!\diagup_1}y=9x-(9)(2)\\\\y=9x-18[/tex]
