Domain and range of a function:
The set X is known as the domain of the function. 'ƒ' and set Y is known as the co-domain. The group of the image of all components of X under the function 'ƒ' is known as the range of 'ƒ' and is shown by ƒ(x). It is clear that range should be a subset of co-domain as we can have few components in co-domain which are not the images of any element of the set X.
Therefore range of 'ƒ' i.e. ƒ(x) = {ƒ(x): x ∈ X}. Clearly ƒ(x) ⊆ Y
Illustration: Calculate the domain of 
Key concept: Denominator could be non-zero for any function
Solution: x2 - 4 ≠ 0 => x ≠ ± 2
Therefore domain is R - {-2, 2}
Illustration: Calculate the domain of 
Key concept: Expression under given even root (i.e. square root, fourth root, sixth root etc) could not be negative.
Solution: f(x) is described when 
....(1)
Case 1: x ≥0 ƒ(x) = x/x-1
For domain 
x∈[0,1).......(2)
Case 2: x < 0 
For domain 
Rejecting the values of x∈[0,∞) because they don't assure the inequality
x < 0.
We obtain x∈(-∞,-1)......(3)
Taking union of (2) and (3)
Domain =
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