#Continuity Question
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I guess could take points and use Bolzano's theorem. For example g(x)=x⁹-f(x) g(0)=-f(0)<0 and g(1)=1-f(1)>0
I guess in case you cannot find a negative and a positive value of g then you would have to build the inequality from 0<f(x)<1 and see whats the upper and lower bounds of g in (0,1)
No it doesn't.