definition of a function

The Definition of a Function in mathematics can be given as representation of relationship between a Set of variables and constants. These are used to solve equations for unknown variables. A function possesses unique output or value for each and every input given to it. A function in its simplest form can be written as: y = x. For any value of 'x' we insert in the function, same will be value of 'y'. So, here 'y' can be said to be dependent on 'x'. Mostly complex Functions involve mathematical operations being applied to 'x' to determine final value of 'y'. For example, if we take y = x2 + 5x + 6. Here, first we need to simplify the function in 'x' using Factorization method. Then for two possible values of 'x' we get two values of 'y'. In functions, values will change, but relationship between variables remains constant.
 
A much known form to represent a function is: f(x).
 
Mostly functions are written with f(x) in place of 'y'. For example, f (x) = 4x. In this notation, function of 'x' is equal to four times value of 'x'. So, for any value of 'x' say 2, function of 'x', or f(x) is equal to 8.
Evaluating a function means solving a mathematical problem or equation involving a function. For this we need to provide an input. For each input given for variable 'x', there can be only one output for function.
For example, in function f(x) = 20x, inputs may be given as:
x = 2,
x = 3,
x = 5,
and corresponding values or outputs of functions that we get will be:
x=2, f(x) = 40,
x=3, f(x) = 60,
x=5, f(x) = 100,
Functions are of importance in various fields of maths, physics, science etc.