Today is our topic of discussion Function of Higher Mathematics .
Function of Higher Mathematics
Relation
We often consider different types of relations among the elements of set X or among the elements of set X and set Y. For example, greater-lesser relation in the set of natural numbers, brother-sister relation in a family, relation of age with your classmates in your recent birthday. For further information regarding this context, please refer to the Mathematics book of class 9-10.
Definition 4 (Relation).
if two sets are X and Y, any subset of their cartesian product set X x Y is called relation from X to Y. So, R⊆X x Y is a relation from X to Y.
Function
The idea of function is as important as sets in mathematics. In practical need, relations between two variables or two sets are considered.
Definition 5 (Function).
If X and Y are sets and under any rule, every element of set X is associated with one and only one element of set Y, that rule is called a function described from X to Y. These types of functions are indicated with symbols such as f, g, F, G etc.
Definition 6 (Domain and Codomain).
If ƒ is a function from set X to set Y, then this is expressed as f: X→ Y. X set is called domain of function f: XY, while set Y is called codomain.
Definition 7 (Image and Preimage).
If under function ƒ : X → Y, x = X is associated with y Є Y, then y is called image of x and x is called preimage of y under this function and it is expressed as y = f(x).
Definition 8 (Range).
Under function f: X→ Y, the set of the elements of Y which are the images of any element of X is regarded as range of function f and it is expressed as “range f”. So, range ƒ = {y: y = f(x) where x = X} = {f(x) : x Є X}. To be noted that range ƒ is the subset of codomain Y.
the domain of the function, domain f Z and range of the function, range = f = {y: y=2x+1, x € Z} is the set of all odd integers.
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