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Math Help - Possibly an intermediate value theorem proof, but I'm not sure.

  1. #1
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    Possibly an intermediate value theorem proof, but I'm not sure.

    Question:

    Suppose that f:[a,b]→ℝ and g:[a,b]→ℝ are continuous functions such that f(a)≤g(a) and f(b)≥g(b). Prove that f(c)=g(c) for some c∈[a,b].

    Intermediate value theorem? Pinching Theorem? I'm not sure on this one.
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  2. #2
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    Re: Possibly an intermediate value theorem proof, but I'm not sure.

    Quote Originally Posted by CountingPenguins View Post
    Suppose that f:[a,b]→ℝ and g:[a,b]→ℝ are continuous functions such that f(a)≤g(a) and f(b)≥g(b). Prove that f(c)=g(c) for some c∈[a,b].
    Use the Intermediate value theorem on h(x)=g(x)-f(x).
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