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