Question

If ƒ(x ) = 2x, then ƒ -1(x ) =s

Answer 1

what do you need to find?

Answer 2

If you have a function
\(\Large\color{blue}{ f(x)=\color{orangered}{\rm k}x}\)
(where K is a constant)

The steps you take in general:
1) replace y with f(x)
2) replace x and y with each other (write x instead of y and vice versa)
3) solve for y (not by replacing it back with x, but by math manipulations)
4) once you isolated y, denote the y as \({\rm f^{-1}(x)}\)
----------------------------------------------------------------

In your case, you are dealing with:
\(\large\color{blue}{ f(x)=\color{orangered}{\rm k}x}\)


step 1: \(\large\color{blue}{ y=\color{orangered}{\rm k}x}\)


step 2: \(\large\color{blue}{ x=\color{orangered}{\rm k}y}\)


step 3: \(\large\color{blue}{ \displaystyle\frac{x}{\color{orangered}{\rm k}}=y}\)


step 4: \(\large\color{blue}{ \displaystyle\frac{x}{\color{orangered}{\rm k}}={\rm f}^{-1}(x)}\)