Question: Consider the function f : R R with f(x) = x if x is rational; 1 if x is irrational. (a) Show that f(x) is

Consider the function f : R R with

f(x) = x if x is rational;

1 if x is irrational.

(a) Show that f(x) is continuous at x = 1.

(b) Show that f(x) is not continuous at x = 0.

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