Study Domain and Range

The study about domain or input of a function f(x) is the total set of possible values of the independent variable in the function. The domain can also be given explicitly. The domain should be always x-values, and the range should be always y-values. The domain has not influenced by anything because it is an independent variable.

The study about range of a function is the total set of all feasible consequential values of the dependent variable of a function. The total set of all possible resulting values of the the range of function is the dependent variable of a function, after we have substituted the values in the domain.


Examples on study domain and range



Ex:1 find the domain and range of the following relation.
{(1, –4), (6, 5), (4, –1), (2, 6), (5, 3)}

Sol:

The domain should be always x-values, and the range should be always y-values. Therefore domain and range of given function is

Domain= {1, 2, 4, 5, 6}

Range= {–4, –1, 3, 5, 6}

Ex:2 State the domain and range of the following relation.
{(–4, 2), (5, 3), (–1, 1), (0, 5), (7, 5), (8, 5)}

Sol:

The domain should be always x-values, and the range should be always y-values

{(–4, 2), (5, 3), (–1, 1), (0, 5), (7, 5), (8, 5)}

domain:  {–4, –1, 5, 7, 8}

range:  {1,2,3,5}


STUDY DOMAIN AND RANGE OF TRIGONOMETRY FUNCTION


Ex:1 Let A = {1, 2, 3, 4} and B = {1, 4, 9, 16, 25}, Find the Domain and Range.

Consider the rule f: A → B: f (x) = x2 for all x Є A.

Then, each element in A has its unique image in B. So, f is a function from A to B.

f (1) = 12 = 1, f (2) = 22 = 4, f (3) = 32 = 9, f (4) = 42 = 16.

Domain(f) = {1,2,3,4} = A, co-domain(f) = {1,4,9,16,25} = B and range(f) = {1,4,9,16}.

Clearly, 25 Є B does not have its pre-image in A.

Ex:2 Let N be the set of all natural numbers. Find the domain and range for the function f(x)=2x.

Let f: N→ N: f(x) = 2x for all x fit in to N

Then, every element in N has its unique image in N.

So, f is a function from N to N.

Clearly f(1)= 2,f(2) = 4,f(3) = 6……., and so on.

Domain(f) = N, Co-domain(f) = N, Range(f) = {2, 4, 6, 8, 10}.