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kathrynag
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Homework Statement
Suppose f: E--> R is cont at x0 and x0 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 x0. Show by example that the continuity of g at x0 need not imply the continuity of f at x0.
Homework Equations
lx-x0l<delta
lf(x)-f(x0)l<epsilon
The Attempt at a Solution
lx-x0l<delta
lg(x)-g(x0)l<epsilon
lf(x)-f(x0l<epsilon
Ok, then it's continuous because g(x)=f(x)?