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Math Help - Intermediate Value Theorem

  1. #1
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    Intermediate Value Theorem

    Need some help.
    Suppose that f: [0,2] -> [0,4] is continuous. Use the IVT to show that there is an x in [0.2] such that f(x)=2x.

    Was given this hint to try and use g: [0,2] -> R defined by g(x)= f(x)-2x. this doesn't seem to help me much.

    Any help would be greatly appreciated!
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  2. #2
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    g(0)\ge 0\ge g(2) Is this correct?
    Does that imply \left( {\exists a \in [0,2]} \right)\left[ {g(a) = 0} \right]?
    Does that help?
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