Q. 3 J

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


Answer :


We know the square of a real number is never negative.


Clearly, f(x) takes real values only when x2 – 16 ≥ 0


x2 – 42 ≥ 0


(x + 4)(x – 4) ≥ 0


x ≤ –4 or x ≥ 4


x (–∞, –4] [4, ∞)


Thus, domain of f = (–∞, –4] [4, ∞)


When x (–∞, –4] [4, ∞), we have x2 – 16 ≥ 0


Hence,


f(x) [0, ∞)


Thus, range of f = [0, ∞)


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