How to find Domain and Range of a given function

How to find Domain and Range of a given function:

If we have given a function f in the form of ordered pair then we can directly find the domain and range, set of fist element of all pair will be a set of domain and second element of all pairs will be a set of Range.

Example:

Given function :  f = (1,2),(1,3),(1,4),(5,2),(5,3),(5,4),(7,2),(7,3),(7,4)

Domain is {1, 5, 7} and Range is {2, 3, 4}

 

If we have given a function f in the form of equation ( x and y form)then we can find the value of y by putting some values of x, here set of all values of x for which y is defined is domain and set of all values y is Range.

Example:

Given function f :  x + y = 7 , where x,y є N

If x = 1, then 1 + y = 7 => y = 6

If x = 2 then 2 + y = 7 => y = 5

If x = 3 then 3 + y = 7 => y = 4

If x = 4 then 4 + y = 7 => y = 3

If x = 5 then 5 + y = 7 => y = 2

If x = 6 then 6 + y = 7 => y = 1

If x = 7 then 7 + y = 7 => y = 0 (0 is not a natural number)

So Domain = {1,2,3,4,5,6}  and  Range = {6,5,4,3,2,1}

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