Prove/disprove: $f^2+f+1$ is not continuous at $x_0$

real-analysis calculus limits continuity

Assume that it is, then $(f^{3}-1)/(f^{2}+f+1)=f-1$ is continuous at $x_{0}$, which in turn implies that of $f$, a contradiction.


You are correct. The premises (are contradictory)[https://math.stackexchange.com/questions/3065701/can-a-cube-of-discontinuous-function-be-continuous/3065705] so the statement is trivially true.

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