Suppose $f(z)$ is an entire function such that $|\overline{f(z)} - 3 - 4i|\le 5$ for all $z \in \mathbb{C}$ and $f(0) = 3$. Evaluate $$\int_{|z| = 1} \frac{f(z)}{z}dz$$
I think the answer is $2\pi if(0) = 6\pi i$ according to Cauchy integral formula but if this would be true then the given inequality is useless. So what's the problem of my answer?