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??