Domain and range of a function

Understand Domain and range of a function

Domain and range of a function- The set X is called the domain of the function. ‘ƒ’ and set Y is called the co-domain. The set of the image of all elements of X under the function ‘ƒ’ is called the range of ‘ƒ’

The set X is called the domain of the function. ‘ƒ’ and set Y is called the co-domain. The set of the image of all elements of X under the function ‘ƒ’ is called the range of ‘ƒ’ and is denoted by ƒ(x). It is obvious that range could be a subset of co-domain as we may have few elements in co-domain which are not the images of any element of the set X. Check out Maths Formulas and NCERT Solutions for class 12 Maths prepared by Physics Wallah. 

Thus range of ‘ƒ’ i.e. ƒ(x) = {ƒ(x): x ∈ X}. Clearly ƒ(x) ⊆ Y 

QUESTIONS BASED ON DOMAIN OF A REAL VALUED FUNCTION

Question 1: Find the domain of

Theory Applied: Denominator should be non-zero for any function

Detail Explanation :    x² – 4 ≠ 0 ⇒ x ≠ ± 2

Hence domain is R – {–2, 2}

Question 2: Find the domain of

Theory Applied:     Expression under even root (i.e. square root, fourth root, sixth root etc) should not be negative.

Detail Explanation :    f(x) is defined when ….(1)

Case 1:    x 0

For domain

    …….(2)           

Case 2:     x < 0     

For domain

Rejecting the values of xbecause they don’t satisfy the inequality x < 0.

We get ……(3)

Taking union of (2) and (3) 

Domain =

Question 3:     Find the domain of .

Theory Applied:     is defined for values of x at which f(x)>0 and g(x)>0 1.

Detail Explanation :        and    

          and   

Hence the domain is