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Tool to calculate the reciprocal of a function f, i.e. the inverse function f-1 which applied to the first function returns the initial value x.

Answers to Questions

What is a reciprocal function? (Definition)

The reciprocal of a function $ f $ is written $ f^{(-1)} $ is such that the following equation is true: $$ f^{(-1)}(f(x)) = x $$

Example: The reciprocal of the exponential function $ \ exp (x) $ is the natural logarithm function $ \ln(x) $ because $ \exp( \ln (x) ) = x $

Although the reciprocal function is denoted with $ ^ {- 1} $ as the inverse $ 1/x $ function, be careful not to confuse the two.

How to calculate an inverse function?

To find the expression of the inverse of a function $ f(x) $, express $ x $ as a function of $ f(x) $ (to facilitate calculations, write $ f(x) = y $)

Example: To calculate the reciprocal of $ f(x) = y = 2x $, it is to calculate $ x = y/2 $ therefore the reciprocal of $ f^{(-1)}(x) = x/2 $, which checks $ f^{(-1)}(f(x)) = (2x)/2 = x $

What function is its own reciprocal function?

The inverse function $ f (x) = 1 / x $ is its own reciprocal function, it is said to be involutive.

Example: $ f(1/x) = 1/(1/x) = x $

How to graphically plot a reciprocal function?

On a graph, the curve of an inverse function $ f ^ {(- 1)} $ is the symmetrical curve of the curve $ f $ with respect to the diagonal axis $ y = x $.

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