Confused about the domain of this function

The textbook seeks the domain of $f/g$, where $ f(x)= \sqrt {x }$ and $g(x) = |x-3|$. The answer stated is $(0,\infty]$. I have two questions here:

1. Shouldn't $3$ be excluded from the domain as one can't divide by zero?
2. Is it okay to use square brackets for infinity? I have never seen infinity included in the domain of any function before, and my teacher clearly stated that infinity is always followed by a parenthesis, not a square bracket. The answer to a similar problem seeking the domain of $g(x) = |x-3|$ is (-$\infty$,$\infty$]. How? Please explain this as well.
   

Solution 1:

You are correct on both counts, and are missing one other count. Because $f$ is defined at $0$, and $g$ is defined and nonzero at $0$, $\frac fg$ is also defined at $0$.

The expression $\frac{\sqrt{x}}{|x-3|}$ is defined for values of $x\in[0,3)\cup(3,\infty)$. Your textbook sounds weird and might be using some nonstandard notation, but without knowing the textbook, I can't be the judge of that.