# Reciprocal Function – Graph, Definition, Domain and Range

Here you will learn what is reciprocal function with definition, graph and domain and range.

Let’s begin –

## Reciprocal Function

The function that associates a real number x to its reciprocal $$1\over x$$ is called the reciprocal function. Since $$1\over x$$ is not defined for x = 0. So, we define reciprocal function as follows :

Definition : The function f : R – {0} $$\rightarrow$$ R defined by f(x) = $$1\over x$$ is called the reciprocal function.

## Graph of Reciprocal Function

The sign of 1/x is same as that of x and 1/x decrease with increase in x.

So, the graph of f(x) = $$1\over x$$ is :

## Domain and Range of Reciprocal Function

Clearly, the domain of this function is R – {0} and its range is also R – {0}.

Domain : R – {0}

Range : R – {0}