Continuous function f(f(x))=1 integral values

2175ExpertCalculusFunctions

Harvard-MIT Mathematics Tournament

Let $f:[0,1] \rightarrow [0,1]$ be a continuous function such that $f(f(x)) = 1$ for all $x \in [0,1]$. Determine the set of possible values of $\int_{0}^{1} f(x) \, dx$.

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Continuous function f(f(x))=1 integral values

2175ExpertCalculusFunctions

Harvard-MIT Mathematics Tournament

Let $f:[0,1] \rightarrow [0,1]$ be a continuous function such that $f(f(x)) = 1$ for all $x \in [0,1]$. Determine the set of possible values of $\int_{0}^{1} f(x) \, dx$.

0 students attempted0% solvedRating 2175