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Optimal solution

If $f(x)$ is a given real valued function, then how to find the minimum value of $x>0$ such that either $\frac{1}{f(x)}>5$ or $f(x)=0.$ If no such $x$ exist then it should return $\infty$ as output. If anyone write the sage code for me by considering any real valued function it would be helpful for me. Thank you in advance.