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