Function
A relation is a rule of correspondence between two
serts, that assigns to each element of the first set at least one
element in the second set. The first set is called the Domain and
the second set is called the Range. Thus you can consider that any
set of ordered pairs is a relation.
Ex
1: The correspondence R, defined by 1R5, 2R3, 2R7, 4R 8,
5R8 is a relation..
This
relation R, has Domain = {1,2,4,5} Range = { 5,3,7,8}and it can
be written as
R =
{(1,5), (2,3), (2,7), (4,8), (5,8)}
A function is a relation that assigns each element in the domain
exactly one elemrnt in the range.
Remark: Letters f, g, h… are usually used to represent functions
and f(x) is used to represent the value the function that assigns
to x.
The relation R in the above example is not a function since 2 has
assigned 3 and 7.
Remark: Letters f,g, h… are usually used to represent functions
and f(x) is used to represent the value that the function assigns
to x.
Ex
2: The function defined by ,
for x a real number, is usually written as
f(x) =2x+1. Find f(2), f(0) & f(3).
Sol:
