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# Help Me! Functions, limits and continuity

Hey guys,

Today I came across a question about the function $$f(x)$$, which takes the value $$x$$ when $$x \in Q$$ and the value $$1-x$$ when $$x \notin Q$$. Is this function continuous at any point?

I thought that $$f(x)$$ would be continuous at $$x=0.5$$ since the left and right hand limits seem to approach $$0.5$$ near $$x=0.5$$.

Am I correct? If so, why? If not, why?

Thanks!

Note by Raj Magesh
2 years, 3 months ago

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