If ƒ(x ) = 2x, then ƒ -1(x ) =s

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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If ƒ(x ) = 2x, then ƒ -1(x ) =s

Algebra
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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

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