Strange proposition in calculus

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  • #1

Homework Statement



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)]

Homework Equations



Intermediate Value Theorem

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??
 

Answers and Replies

  • #2
119
0
I think the question is asking you to show that the range on [a,b] is [f(a),f(b)]
 
  • #3
Ah... that makes sense...
 

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