# How do I find the discontinuity of the function $f(x) =\cos (x/(x - \pi))$?

I need help in finding the discontinuity of the function:

$$f(x) = \cos \left(\frac{x}{x - \pi}\right)$$

Any comments or advice will be much appreciated.

Thanks.

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Wouldn't that just be at x=pi where the function is undefined, or is there something more to this question? –  Peter Grill Mar 14 '12 at 18:21
Do you mean: $\cos \frac{x}{x-\pi}$? Under normal notation $x/x-\pi = (\frac{x}{x})-\pi$, which is probably not what you want. –  Thomas Andrews Mar 14 '12 at 18:22
I formatted your question using LaTeX. Please check to make sure the new version is what you intended to ask. –  Alex Becker Mar 14 '12 at 18:22
There is no need to add a "signature" at the end of your post; the post will include your name at the bottom right automatically. –  Arturo Magidin Mar 14 '12 at 18:24
@AlexBecker It is probably not wise to reformat his question to assume he meant what the normal order of operations meant. It gives false clarity to later people trying to answer the question, when your reformat obscures the likelihood that he mis-entered the question. –  Thomas Andrews Mar 14 '12 at 18:25

## 2 Answers

There is no discontinuity check http://www.wolframalpha.com/input/?i=cos%28x%2F%28x-pi%29%29, also it is not defined at $x=\pi$ as the other answer describes.

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Thanks for the feedback Kirthi –  Xavier Mar 15 '12 at 0:13

There is no discontinuity in this function, but there is a point where the function is not defined, namely $x=\pi$, because $\frac{\pi}{\pi-\pi}=\frac{\pi}{0}$ is undefined.

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Thats right, the new version is what I intended to ask. I am so sorry for the confusion as I am new to this forum. –  Xavier Mar 14 '12 at 18:29