Q. 2 B4.0( 6 Votes )

# Find the domain of each of the following real valued functions of real variable:

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

Clearly, f(x) takes real values only when x2 – 1 ≥ 0

x2 – 12 ≥ 0

(x + 1)(x – 1) ≥ 0

x ≤ –1 or x ≥ 1

x (–∞, –1] [1, ∞)

In addition, f(x) is also undefined when x2 – 1 = 0 because denominator will be zero and the result will be indeterminate.

x2 – 1 = 0 x = ±1

Hence, x (–∞, –1] [1, ∞) – {–1, 1}

x (–∞, –1) (1, ∞)

Thus, domain of f = (–∞, –1) (1, ∞)

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