(i) f(x) = –|x|, x ∈ R
We know that
|| = { , ≥ 0; −, < 0
∴ () = −|| = { −, ≥ 0 ; , < 0
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) () = √(9 − 2)
Since √(9 − 2) 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].