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Math Help - Continuity

  1. #1
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    Continuity

    Definition: a function f is very continuous if for every epsilon>0 there exists a delta>0 s.t. whenever x and t are in the domain of f and absolute value(x-t)<delta, we get absolute value(f(x)-f(t))<epsilon.

    Prove: Let f and g be very continuous where f and g have the same domain. What can be said about f+g?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by spikedpunch View Post
    Definition: a function f is very continuous if for every epsilon>0 there exists a delta>0 s.t. whenever x and t are in the domain of f and absolute value(x-t)<delta, we get absolute value(f(x)-f(t))<epsilon.

    Prove: Let f and g be very continuous where f and g have the same domain. What can be said about f+g?
    Hint: Triangle inequality.
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