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)]
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??