Q. 3 G

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

f(x) = –|x|

Answer :

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, ∞)


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