CAT Domain of function, Co-domain, Range of function - Practice Questions & MCQ

Domain

All possible values of x for f(x) are defined (f(x) is a real number) and is known as Domain.

If a function is defined from A to B i.e. f: A⇾B, then all the elements of set A is called Domain of the function. 

Co-domain

If a function is defined from A to B i.e. f: A⇾B, then set B is called Co-domain of the function. 

Range

The set of all possible values of f(x) for every x belonging to the domain is known as Range of this function.

For example, let A = {1, 2, 3, 4, 5} and B = {1, 4, 8, 16, 27, 64, 125}. The function f : A -> B is defined by . So here,

Domain : Set A

Co-Domain : Set B

Range : {1, 8, 27, 64, 125}

The range is always a subset of the co-domain and Range can be equal to co-domain in some cases.

Note: If only the formula is given, then the co-domain is R, and domain and range have to be found.

• Domain, in this case, will be all the real values of x for which y is real
• Range is all the real values of y corresponding to values of x in the domain

Rules to find Domain

• If the domain of f(x) is A and the domain of g(x) is B, then the domain of f(x)+g(x), f(x) - g(x), f(x) . g(x) is A ∩ B.
• For domain of f(x)/g(x), remove values of x for which g(x)=0, from A ∩ B.
• Domain of expressions of type  , we take the common values between A and values of x for which f(x) ≥ 0.
• Domain of the polynomial function is R.
• Graphical method: we can also find a domain if only the graph of function is given. We will learn this through the help of solved examples.

Methods to find Range

• Simple manipulations
• For the range of y = f(x), we can first express x as a function of y: x = g(y). Now the domain of x = g(y) is same as the range of y = f(x)
• Graphical method: we can also find the range if only the graph of the function is given.