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in Sets, Relations and Functions by (27.7k points)
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Mark (√) against the correct answer in the following: 

Let f(x) = log (1 – x) + √x2 – 1. Then, dom (f) = ? 

A. (1, ∞) 

B. ( - ∞, - 1] 

C. [ - 1, 1) 

D. (0, 1)

1 Answer

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Best answer

Correct Answer is (B) ( - ∞, - 1]

log (1 – x) + √(x2 – 1)

1 - x > 0

x < 1

x2 - 1 ≥ 0

x2 ≥ 1

⇒ -1 ≤ x ≥ 1

Taking intersection of the ranges we get

Dom (f) = (b) ( - ∞, - 1]

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