The domain of definition of the function f(x) = \(\sqrt{\frac{x-2}{x+

1.	The domain of definition of the function f(x) = \(\sqrt{\frac{x-2}{x+2}}\) + \(\sqrt{\frac{1-x}{1+x}}\) is A. (-∞, -2] ∪ [2, ∞) B. [-1, 1] C. ϕ D. None of these
Answer» Option : (C) Given, f(x) = √((x-2)/(x+2))+√((1-x)/(1+x)) For function to be defined, \({\frac{x-2}{x+2}}\) ≥ 0, x ≠ - 2 x∈(-∞,-2)∪[2, ∞) …(1) And, \({\frac{1-x}{1+x}}\) ≤ 0 So, Taking common of both the solutions, we get x ∈ ϕ.

The domain of definition of the function f(x) = \(\sqrt{\frac{x-2}{x+2}}\) + \(\sqrt{\frac{1-x}{1+x}}\) is A. (-∞, -2] ∪ [2, ∞) B. [-1, 1] C. ϕ D. None of these

Answer»

Option : (C)

Given,

f(x) = √((x-2)/(x+2))+√((1-x)/(1+x))

For function to be defined,

\({\frac{x-2}{x+2}}\) ≥ 0, x ≠ - 2

x∈(-∞,-2)∪[2, ∞) …(1)

And,

\({\frac{1-x}{1+x}}\) ≤ 0

So,

Taking common of both the solutions, we get

x ∈ ϕ.