**11. What is the value of[x] + [-x] where x is a real number?
Solution: **

We consider the following expression

[x]+[-x]

We consider following two cases

**Case 1**

If x is an integer, then so is -x

Also,

[x]=x

[-x]=-x

Therefore,

[x]+[-x]=x+(-x)

=x-x

=0

**Case 2**

If x is not an integer, then so is not -x

Let us take x to be a rational number, that is,

x=1/p

Where p\neq0,-1,1

And is an integer

Therefore,

[x]+[-x]=[1/p]+[-1/p]

=0+(-1)

=-1