Question

What is the inverse of the function f(x) =
1/9x+ 2?

Answer 1

`f^(-1)(x) = 9x -18.`

Explanation:

`y=f(x)=\frac 19 x +2\\\\\text{Replace x with y and then solve for y,}\\\\~~~~~~~x = \frac 19 y+2\\\\\implies 9x =y + 18~~~~~~~~~~~~~~~;[\text{Multiply both sides by 9}]\\ \\\implies y = 9x -18\\\\\implies f^(-1)(x) = 9x -18\\\\\text{Hence, the inverse of the given function is}~ f^(-1)(x) = 9x -18.`