Reciprocal functions are mathematical functions defined as the inverse of a given function. For a function f(x) , its reciprocal function is expressed as g(x) = \frac1f(x) . This means that for every output of the original function, the reciprocal function provides the multiplicative inverse. These functions are often represented graphically, showing a hyperbola shape. The reciprocal function is undefined when f(x) = 0 , leading to vertical asymptotes in the graph. Common examples include the reciprocal of linear functions, such as g(x) = \frac1x , which is a fundamental concept in algebra and calculus.