5. For each x = [0, 1], let f(x) = x if x is irrational, and let f(x) = 1 x if it is rational. Find where in [0, 1] the function is continuous. Show that f(f(x)) = x for every x = [0, 1]. Show that f assumes every value in [0.1].

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Author:Erwin Kreyszig
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5. For each x = [0, 1], let f(x) = x if x is irrational, and let f(x) = 1 - x if it is rational.
Find where in [0, 1] the function is continuous.
Show that f(f(x)) = x for every x = [0, 1].
Show that f assumes every value in [0.1].
Transcribed Image Text:5. For each x = [0, 1], let f(x) = x if x is irrational, and let f(x) = 1 - x if it is rational. Find where in [0, 1] the function is continuous. Show that f(f(x)) = x for every x = [0, 1]. Show that f assumes every value in [0.1].
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