**(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].