# discontinuity of a absolute value piece wise function

So I have this piecewise function here:

$f(x) = \left\{ \begin{array}{ll} \cos(\frac{\pi x}{2}), & \ \ |x| < 1 \\ \ |x-1|, & |x|\geq 1 \end{array} \right.$

I know that I can use the definition of continuity to do this question and find that the definition does not hold at x=1 but the absolute values are throwing me off. How would I exactly deal with that? This would be really easy if the absolute value isn't in the domain.

Any ideas?

• check $x=+1, -1$. – R.N Sep 26 '16 at 9:43
• I get that at 1, the definition hold and that at -1 it does not hold since the two sided limits do not equal to each other so -1 is a point of discontinuity I believe. – Future Math person Sep 26 '16 at 9:53
• You are right . – R.N Sep 26 '16 at 9:54
• you'r welcome . – R.N Sep 26 '16 at 9:56