Question -
Answer -
(i) Given,
f(x) = –|x|, x ∈ R
We know that,
As f(x)is defined for x ∈ R, the domain of f is R.
It is also seen thatthe range of f(x) = –|x| is all real numbers exceptpositive real numbers.
Therefore, the rangeof f is given by (–∞, 0].
(ii) f(x) = √(9 –x2)
As √(9 – x2) isdefined for all real numbers that are greater than or equal to –3 and less thanor equal to 3, for 9 – x2 ≥ 0.
So, the domainof f(x) is {x: –3 ≤ x ≤ 3} or [–3,3].
Now,
For any value of x inthe range [–3, 3], the value of f(x) will lie between 0 and3.
Therefore, the rangeof f(x) is {x: 0 ≤ x ≤ 3} or [0, 3].