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.

Explanation

The given function g(x) is defined at all integral points

Let n be an integer

Then `g(n)=n−n=n−n=0`


L.H.L. at `x=n=lim_(x->n^(−))g(x)=lim_(x->n^(−))(x−[x])=n−(n−1)=1`


R.H.L. at `x=n=lim_(x->n^(+))g(x)=lim_(x->n^(+))(x−[x])=n−n=0`


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