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

To show that the function defined by \( g(x) = x \cdot [x] \) is discontinuous at all integral points, we will analyze the behavior of the function at an integer \( k \). Here, \( [x] \) denotes the greatest integer less than or equal to \( x \).

### Step-by-Step Solution:

1. **Define the Function**:
The function is given by:
\[
g(x) = x \cdot [x]
...