we have
\(f(x)=\frac{1}{9}x-2\)
Let
\(y=f(x)\)
\(y=\frac{1}{9}x-2\)
To find the inverse
Exchanges the variables x for y and y for x
\(x=\frac{1}{9}y-2\)
Isolate the variable y
Multiply by \(9\) both sides
\(9x=y-18\)
Adds \(18\) both sides
\(9x+18=y-18+18\)
\(y=9x+18\)
Let
\(f^{-1}(x)=y\)
\(f^{-1}(x)=9x+18\) -------> the inverse function
therefore
the answer is
\(f^{-1}(x)=9x+18\)
