Question 2:
Find the domain and range of the following real function:
(i) f(x) = −|x|
Answer
(i) f(x) = −|x|, x ∈ R
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].
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].
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