Question

Find the domain and range of the following real function:
(i) f(x) = –|x|
(ii) () = √(9 − x²)

Answer 1

(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].

(ii) () = √(9 − x²)
Since √(9 −x²) 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].