Let $f(x) = \frac{1- \tan x}{4x - \pi}, \; x \neq \frac{\pi}{4} , \; x \in [0, \frac{\pi}{2}]$. If $f(x)$ is continuous in $[0, \frac{\pi}{2}]$, then $f(\frac{\pi}{4})$ is

Question

( A ) $-\frac{1}{2}$
( B ) $-1$
( C ) $\frac{1}{2}$
( D ) $1$