to
represent functions was made by Leonhard Euler (1707-1783) in 1734 in the first
part of his manuscript “Analysis Infinitorium” Later on, Joeph Louis Lagrange
(1736-1813) published his manuscripts “Theorie des functions analytiques” in
1793, where he discussed  about analytic function and used the notion f (x), F(x),
φ(x) etc for different function of x Subsequently, Lejeunne Dirichlet
(1805-1859) gave the definition of function which was being used till the set
theoretic definition of function presently used, was given after set theory was
developed by Georg Cantor (1845-1918)