Reciprocal of a Function

Reciprocal of a Function

The reciprocal relationship of a function f of X in Y is the relation noted f-1, of Y in X, so that, for all elements of the domain of f, if y = f(x), then x = -1(y).

  • When the reciprocal relationship of a function f is also a function, we call it the reciprocal function of f and we say that the function f is invertible.
  • The reciprocal of a function is not necessarily a function.
  • The graph of the reciprocal relationship of a function f is symmetrical to the graph of f in relation to the angle bisector of the first quadrant of the Cartesian plane.


Consider the function f: \(\mathbb{R}\) → \(\mathbb{R}\) : x ↦ x + 2; therefore, \(^{-1}\)(x) : \(\mathbb{R}\) → \(\mathbb{R}\) : xx – 2.

reciproque fonction

Educational Note

The term reciprocal is an adjective that can be applied to many mathematical objects: reciprocal relationship, reciprocal function, reciprocal proposition, etc. For this reason, it is preferable to not omit the word to which it applies in a given context.

Therefore, the reciprocal relationship of the square root function does not have the same meaning as the reciprocal function of the square root function.

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