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 =
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