Q. 3 J

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

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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