Domain of a Piecewise Function

I've got a piecewise function defined as :

$$f(x)=\begin{cases} |2x-1| & x<1\\ x^2-1 & 1 \le x <2\\ \lfloor 3x \rfloor & x \in [2,3) \end{cases} $$

I am trying to find the domain of this function and I haven't been able to find a like example but I believe the domain of this function is just (-∞,3) from reading off from the values but this is incorrect.

If the domain is all possible x values that can be put into f(x) I am unsure how this answer is wrong.

Thank you.

1 Answer

As others have mentioned in comments, your domain is correct. That is, for your piecewise-defined function $f$ you have $\operatorname{Dom}(f)=(-\infty,3)$. However, perhaps you meant to determine the range of $f$ instead. If so, then you should be able to see that $\operatorname{Rng}(f)=[0,\infty)$. If you are certain that your book means domain instead of range, then you must accept the fact that your book is simply wrong (this would not be the first time a math book had a misprint or misinformation).