Q. 3 F3.8( 4 Votes )

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

f(x) = |x – 1|

Answer :

f(x) = |x – 1|


We know


Now, we have



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


Thus, domain of f = R


When x < 1, we have x – 1 < 0 or 1 – x > 0.


Hence, |x – 1| > 0 f(x) > 0


When x ≥ 1, we have x – 1 ≥ 0.


Hence, |x – 1| ≥ 0 f(x) ≥ 0


f(x) ≥ 0 or f(x) [0, ∞)


Thus, range of f = [0, ∞)


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