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## Homework Statement

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}.

## Homework Equations

lx-x

_{0}l<delta

lf(x)-f(x

_{0})l<epsilon

## 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)?