Question

1. f(x)=[x] sin (+1) where [x] denotes greatest integer function. Domain of f(x)

​

Answer 1

Answer:

Correct option is

A

[0,1)

We know that the range of sin  

−1

 is [  

2

−π

​

,  

2

π

​

] and domain is [−1,1]

Now in f(x)=sin(x+[x])

The input should be in the domain [−1,1]

x+[x]≥−1

⇒x≥0

and x+[x]≤1

⇒x≤1

However, [x] is discontinuous at x=1

Hence domain, of f(x)=sin  

−1

(x+[x]) is [0,1)

Step-by-step explanation: