Let . Their *composition* is the function is defined by

*Let and be functions with continuous at some point , and continuous at the point . Then is continuous at .*

**Proof**: *For each , we must find a such that*

Let , since is continuous at , :

But also is continuous at , so (*we can get -close to *), such that

So therefore,

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October 12, 2011 at 12:09 pm

MS 2001: Week 4 « J.P. McCarthy: Math Page[…] The proof ofÂ Proposition 2.3.6. […]