Question

find domain of f(x) = √log_1/2 (x/x²-1)​

Answer 1

Step-by-step explanation:

Function is

conditions for defining function :

1. (x² - 2x + 2) > 0 [ for log to be defined ]

2. [ square root always positive ]

Now , solving inequality 1 ,

x² - 2x + 2 > 0

Here you see coefficient of x² = 1 > 0

But discriminant , D = b² - 4ac = (2)² - 4.2 = -4 < 0

∴ (x² - 2x + 2) > 0 for all real value of x

so, x ∈ R

Solving inequality 2 ,

⇒

⇒

⇒ (x² - 2x + 2) ≤ 1

⇒ x² - 2x + 1 ≤ 0

⇒ (x - 1)² ≤ 0

∵ (x - 1)² ≠ negative

so, (x - 1)² = 0

⇒ x = 1

Now, take common value of x from both cases ,

x ∈ R and x ∈ {1 }

∴ x ∈ {1}

Hence, domain of f(x) ∈ { 1}