Let f(x) = √log (2x – x^2). Then, dom (f) = ?

Question

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

Let f(x) = √log (2x – x²). Then, dom (f) = ? 

A. (0, 2) 

B. [1, 2] 

C. ( - ∞, 1] 

D. None of these

Answer 1

Correct Answer is (C) ( - ∞, 1]

f(x) = √log (2x – x²).

⇒ 2x - x² > 1

⇒ x² - 2x + 1 < 0

⇒ (x - 1)² < 0

⇒ x - 1 < 0

⇒ x < 1 

log(2x - x²) > 0

⇒ 2x - x² > e⁰ = 1

⇒ x < 1

Dom (f) = ( - ∞, 1)