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1. Let [a, b] n E be a closed bounded interval, and let f : [a,b] - [a,b] be a function. Suppose that f is Continuous Prove that there is Some c € [a, b] such that f (c) = c. The number c is called a fixed point of f. 2. Let 1,1 n = be open intervals and let f:1 - = be a function. Suppose that f is Continuous. Let x € f-'()). Prove that there is Some open interval K n = such that

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