Answer:
[tex]f^{-1}(x)=9x+2[/tex]
Step-by-step explanation:
Given: [tex]f(x)=\dfrac{1}{9}(x-2)[/tex]
We need to find the inverse of f(x).
Step 1: Set f(x) = y
[tex]y=\dfrac{1}{9}(x-2)[/tex]
Step 2: Switch x and y
[tex]x=\dfrac{1}{9}(y-2)[/tex]
Step 3: Solve for y, Isolate y
[tex]x=\dfrac{1}{9}(y-2)[/tex]
Multiply by 9 both sides
[tex]9x=y-2[/tex]
Add 2 both sides
[tex]9x+2=y[/tex]
[tex]y=f^{-1}(x)[/tex]
Hence, [tex]f^{-1}(x)=9x+2[/tex]
