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Question 2:
Find the domain and range of the following real function:
(i) f(x) = –|x| (ii) 
(i) f(x) = –|x|, x ∈ R
We know that |x| = 
Since f(x) is defined for x ∈ R, the domain of f is R.
It can be observed that the range of f(x) = –|x| is all real numbers except positive real numbers.
∴The range of f is (–
, 0].
(ii)
Since
is defined for all real numbers that are greater than or equal to –3 and less than or equal to 3, the domain of f(x) is {x : –3 ≤ x ≤ 3} or [–3, 3].
For any value of x such that –3 ≤ x ≤ 3, the value of f(x) will lie between 0 and 3.
∴The range of f(x) is {x: 0 ≤ x ≤ 3} or [0, 3].
