Let the sets A and B denote the domain and range respectively of the function f(x)=1/(√(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, ∞)

(C) neither (S1) nor (S2) is true

(D) both (S1) and (S2) are true

Sets, Relations and Functions: JEE Main 2023 Mathematics question

JEE Main 2023 · 6 Apr, Evening shift · Q3895

JEE Main 20236 Apr, Evening shiftMathematicsHardSets, Relations and Functions168× since 2002

Let the sets A and B denote the domain and range respectively of the function

f(x)=\frac{1}{\sqrt{\lceil x\rceil-x}}

, where

\lceil x\rceil

denotes the smallest integer greater than or equal to

x

. Then among the statements (S1) :

A \cap B=(1, \infty)-\mathbb{N}

and (S2) :

A \cup B=(1, \infty)