Question

Find the domain and range of each of the following real valued functions : 

f(x) = –|x|

Answer 1

f(x) = –|x|

We know,

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, ∞)