Suppose that a function is continuous on the closed interval 0, 1 and that 0 (x) 1 for every x in 0, 1 Show that there must exist a number c in 0, 1 such that (c) c (c is called a fixed point of )

Question: Suppose that a function is continuous on the closed interval [0, 1] and that 0 (x) 1 for every x in [0,

Suppose that a function ƒ is continuous on the closed interval [0, 1] and that 0 ≤ ƒ(x) ≤ 1 for every x in [0, 1]. Show that there must exist a number c in [0, 1] such that ƒ(c) = c (c is called a fixed point of ƒ).

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