Functions in economics
The concept of function has special significance in economics. Generally, the various laws and theories of economics are expressed in the form of functions. Some of the important functional relationships are: demand function, supply function, cost function, etc. The above figure shows the graphs of demand and supply functions in economics.
## Functions

**Definition of a function: **Let A and B be two non-empty sets. A function 'f' from A to B, written as f : A B, is a relation in which every element 'x' of A corresponds to only one element f(x) of B. The element f(x) is called the **image** of 'x' and the element 'x' is called the **pre-image** of f(x). The ordered pairs of a function 'f' are represented as (x, f(x)).

**Domain, co-domain and range of a function: **Let 'f' be a function from non-empty set A to another non-empty set B. Then, the non-empty set A is called the ‘domain’ of the function 'f', the non-empty set B is called the ‘co-domain’ of the function 'f' and {f(x): x A} B is called the ‘range’ of the function. In some cases, the range happens to be identical with the coâ€“domain of a function.

**Ex: **Let A = { – 1, 1, 2, 3, 4} and B = {1, 4, 9, 16, 24} and the rule f(x) = x^{2}, x A is a function from A to B then find domain, co–domain and range of a function.

**Sol: ** Given, f: A B is a function. Using the rule f(x) = x^{2}, x A we have:

f(–1) = (–1)^{2} = 1; f(1) =
(1)^{2} = 1; f(2) =
(2)^{2} = 4; f(3) =
(3)^{2} = 9; f(4) =
(4)^{2} = 16

∴ Domain of a function = A = {– 1, 1, 2, 3, 4};

Co-domain of a function = B = {1, 4, 9, 16, 24};

Range of a function = {1, 4, 9, 16}.