Question

Let the sets A and B denote the domain and range respectively of the function f(x) = \(\frac{1}{\sqrt{[x]-x}},\) where [x] denotes the smallest integer greater than or equal to x . Then among the statements

(S₁) : A ∩ B = (1, ∞) – N and 

(S₂) : A ∪ B = (1, ∞)

(1) only (S₁) is true 

(2) both (S₁) and (S₂) are true 

(3) neither (S₁) nor (S₂) is true 

(4) only (S₂) is true

Answer 1

(1) only (S₁) is true