f-z-1-1-z-2-2-z-2-2-1-z-2-2-z-2-f-0-f-1-2-f-1-2-

Question Number 655 by 123456 last updated on 19/Feb/15

f (z) = \frac{1 - \frac{1 - z^{2}}{2 + z^{2}}}{2 + \frac{1 - z^{2}}{2 + z^{2}}}

\frac{f (0) + f (1)}{2} - f (\frac{1}{2}) = ?

Answered by prakash jain last updated on 19/Feb/15

f (0) = \frac{1 - \frac{1}{2}}{2 + \frac{1}{2}} = \frac{1}{5}

f (1) = \frac{1}{2}

f (0) = \frac{1 - \frac{1}{3}}{2 + \frac{1}{3}} = \frac{2}{7}

\frac{f (0) + f (1)}{2} - f (\frac{1}{2}) = \frac{\frac{1}{5} + \frac{1}{2}}{2} - \frac{2}{7} = \frac{7}{20} - \frac{2}{7} = \frac{9}{140}