Q19 of 147 Page 159

Show that the function defined by g(x) = x – [x] is discontinuous at all integral points. Here [x] denotes the greatest integer less than or equal to x.

It is given that g(x) = x – [x]

We know that g is defined at all integral points.


Let k be ant integer.


Then,


g(k) = k – [-k] = k + k = 2k




And





Therefore, g is discontinuous at all integral points.


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