In mathematics, function application is the act of applying a function to an argument from its domain so as to obtain the corresponding value from its range. In mathematics, function application is the act of applying a function to an argument from its domain so as to obtain the corresponding value from its range. Function application is usually depicted by juxtaposing the variable representing the function with its argument encompassed in parentheses. For example, the following expression represents the application of the function ƒ to its argument x.