f(x) = –|x|

We know

Now, we have

Hence, f(x) is defined for all real numbers x.

Thus, domain of f = R

When x < 0, we have –|x| < 0

Hence, f(x) < 0

When x ≥ 0, we have –x ≤ 0.

Hence, –|x| ≤ 0 ⇒ f(x) ≤ 0

∴ f(x) ≤ 0 or f(x) ∈ (–∞, 0]

Thus, range of f = [0, ∞)