Let f(x) = e^√x^2 -1. log(x - 1). then, dom (f) = ?

Question

Mark (√) against the correct answer in the following:

Let f(x) =\(e^\sqrt{{x^2-1}}\). log (x - 1) . then, dom(f) = ?

A. ( - ∞, 1] 

B. [ - 1, ∞) 

C. (1, ∞) 

D. ( - ∞, - 1] ∪ (1, ∞)

Answer 1

Correct Answer is (C) (1, ∞)

f(x) =\(e^\sqrt{{x^2-1}}\) log (x - 1)

x - 1 > 0

⇒ x > 1

And

⇒ x² - 1 ≥ 0

⇒ x² ≥ 1

⇒ -1 ≤ x  ≥ 1

Taking the intersection we get

Dom(f) = (1, ∞)