Answer with explanation:
The given equation which includes greatest integer function
[ x -1 ] = [x ]
Using property of greatest integer functions
⇒ [x ] -1 =[x]
Cancelling [ x ], from both sides, gives
0 = -1,
Which will be not true for any value of x.
⇒⇒
[x]=x -{x}, where x, is positive real number and {x} is fractional part of x.
Also, [x]=x-1+{x}, where x, is any negative real number and {x} is positive fractional part of x.
None of the Option given is true.
