Question
Ā If f(x) is continuous for all real values of
x and f(x) takes on only rational values, then if f(1)=1, the value of f(0) isSolution
Property: - Let f:[0,1]ā R be continuous such that f(x)āQ for any xā[0,1] then f (x) is constant. Proof Suppose f isn't constant. Then for some a,bā[0,1], f(a)ā f(b);Ā Without Loss of Generality, f(a)
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