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 June 5th, 2017, 01:48 AM #1 Senior Member   Joined: Nov 2015 From: hyderabad Posts: 232 Thanks: 2 Empty set If $\displaystyle f : R \rightarrow R$ is a cubic polynomial then $\{x \in R : f(x^3) = \sqrt2\}$ is an empty set ? Thank you in advance
 June 5th, 2017, 07:00 AM #2 Member   Joined: May 2017 From: Russia Posts: 34 Thanks: 5 $\displaystyle (f(x^3)-\sqrt{2})$ is a polynomial of degree 9. It has a root in $\displaystyle \mathbb{R}.$ Thanks from Country Boy

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