Let the sets A and B denote the domain and range respective…

Maths Functions, Limits, Continuity and Differentiability JEE Main 2023 - ( Function ) Single Correct MCQ

Published on: August 13, 2026

Let the sets A and B denote the domain and range respectively of the function , where [x] denotes the smallest integer greater than or equal to x.

Then among the statements

and

Only (S2) is true

Only (S1) is true

Neither (S1) nor (S2) is true

Both (S1) and (S2) are true

Text Solution

Verified by Experts

The correct answer is:

Given,

We know that, x =[x]+{x} where {x} is fractional part of x whose value is 0 <{x}< 1,

So, [x]-x = -{x}

Now putting the value in given function we get,

Now we know that is defined when g(x)> 0, but -{x} (-1, 0)

Hence, is not defined

Hence, Domain and Range will be=

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