(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose f: E--> R is cont at x_{0}and x_{0}is an element of F contained in E. Define g:F--->R by g(x)=f(x) for all x elemts of F. Prove g is continuous at x_{0}. Show by example that the continuity of g at x_{0}need not imply the continuity of f at x_{0}.

2. Relevant equations

lx-x_{0}l<delta

lf(x)-f(x_{0})l<epsilon

3. The attempt at a solution

lx-x_{0}l<delta

lg(x)-g(x_{0})l<epsilon

lf(x)-f(x_{0}l<epsilon

Ok, then it's continuous because g(x)=f(x)?

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# F continuous at x[sub]0[/sub], prove g is continuous atx[sub]0[/sub]

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