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How can the inverse of f(x) = 2x be found?

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A graph of the function f(x) = x cubed minus 3x plus 2 is shown on a blue background, with a red curve passing through key points. Local maximum and minimum points are marked with black dots at x equals negative 1 and x equals 1, illustrating important features of the curve. — function Plot of the cubic equation f(x) = x³ − 3x + 2. The plotted points are where changes in curvature occur.

To find the inverse of a function $f (x) = 2 x$ , you essentially reverse the operation that the function performs. An inverse function is derived by interchanging the variables $x$ and $y$ .12

Follow these steps to solve for the inverse:

Start with the equation: $y = 2 x$
Interchange the variables $x$ and $y$ : $x = 2 y$
Solve the new equation for $y$ :
$y = \frac{x}{2}$

Thus, the inverse function is $f^{- 1} (x) = \frac{x}{2}$ . By applying the original function and then its inverse, you return to the original input value, as the inverse function effectively "undoes" the effect of the original mathematical procedure.1