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?

  • $\begingroup$ check $ x=+1, -1$. $\endgroup$ – R.N Sep 26 '16 at 9:43
  • $\begingroup$ 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. $\endgroup$ – Future Math person Sep 26 '16 at 9:53
  • 1
    $\begingroup$ You are right . $\endgroup$ – R.N Sep 26 '16 at 9:54
  • $\begingroup$ you'r welcome . $\endgroup$ – R.N Sep 26 '16 at 9:56

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