I'm a student studying math, and I'm going through some old exam problems and I have come across a set of questions that ask me to decide where a given piece-wise function is continuous. The function in question is.
$$f(x)= \begin{cases} |x-1| & \text{if }x \geq 0 \\ f(-x) & \text{if }x <0 \\ \end{cases} $$
This function naturally is causing me much confusion. The function seems it will trail of into a infinite string of functions in functions. However If I had to guess its continuity I'd hazard intuitively there appears to be no reason $f(x)$ is not defined across $\mathbb{R}$. Am I right to think this? Is there a rigorous theorem I should be using? And how do I manage this recursive second condition?
Any help would be much appreciated!