2.2.10 (Fixed points) For each of (a)–(e), find an equation x = f(x) with the stated properties, or if there are no examples, explain why not. (In all cases, assume that f(x) is a smooth function.) a) Every real number is a fixed point. b) Every integer is a fixed point, and there are no others. c) There are precisely three fixed points, and all of them are stable. d) There are no fixed points. e) There are precisely 100 fixed points.

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