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Strange proposition in calculus

  1. Oct 12, 2012 #1
    1. The problem statement, all variables and given/known data

    f(x) is an injective function (1 to 1) and continuous in [a, b], and f(a) < f(b). Show that the
    range of f is the interval [f(a), f(b)]

    2. Relevant equations

    Intermediate Value Theorem

    3. The attempt at a solution
    We are asked to use the intermediate value theorem to prove it. However, it seems to me that the proposition is false.

    Suppose f(x) = x, a = 0, b = 1. f(x) is 1 to 1, continuous in [a,b] and f(a) < f(b), but its range is (-inf, inf), not [0, 1].

    Am I reading this question wrong??
     
  2. jcsd
  3. Oct 12, 2012 #2
    I think the question is asking you to show that the range on [a,b] is [f(a),f(b)]
     
  4. Oct 12, 2012 #3
    Ah... that makes sense...
     
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