Which set of numbers best describes the possible values of x in the equation below?

[x-1]=[x]

a) all integer values of x

b) all real number values of x

c) only negative values of x

d) only fractional values of x

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.

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