Mathematics, 03.12.2019 06:31, Kiona3815

Suppose f(x) is continuous on the interval [0,1] with 0< = f(x)< = 1 for all x. prove that f has a fixed point; that is, there exists a c in the interval [0,1] such that f(c) = c. (hint: you need to use the intermediate value theorem on the function h(x) = f(x) – x.)

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Suppose f(x) is continuous on the interval [0,1] with 0< = f(x)< = 1 for all x. prove that f...