Answer
The function $h(x)=x [x]$ is continuous at any real number except nonzero integers.
Work Step by Step
As we know, for any real number $x$ there exists some integer $n$ such that $n \le x \le n+1$, so we can write $h(x)$ as $h(x)=nx$.
Now, for any $x \in (n,n+1)$ the function $h(x)=nx$ is clearly continuous at $x$ (Please note that this function is the restriction of the continuous function $h: \mathbb{R} \to \mathbb{R}, \, h(x)=nx$ to the interval $(n, n+1)$ and we can always choose $\delta n$ we have $n
