If f is an analytic function such that ƒ : |z❘ < 1 → |z❘ < 1. If f(0) = 0, then which of the following may be possible
1
\(\left|f^{\prime}(0)\right|=\sec \frac{\pi}{6}\)
2
\(f\left(\frac{1}{2}\right)=\frac{1}{2}\) and \(f\left(\frac{1}{4}\right)=\frac{1}{3}\)
3
\(f\left(\frac{1}{4} i\right)=\frac{1}{2}+\frac{1}{2} i\)
4
\(\left|f^{\prime}(0)\right| \leq \cot \frac{\pi}{4}\)