## anonymous one year ago If ƒ(x ) = 2x, then ƒ -1(x ) =s

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1. anonymous

what do you need to find?

2. SolomonZelman

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