Question

Range of the function f(x)= [x] where [x] is a greatest integer function​

Answer 1

We've,

[x]=x−{x} for x∈R. Where {x} is the fractional part of x.

Now,

[x]−x=−{x}.

As we've 0≤{x}<1

or, −1<−{x}≤0.

So range of of f(x) is (−1,0]