The value of $f(0)$ so that the function $f(x)=\large\frac{2x-\sin^{-1}x}{2x+\tan^{-1}x}$ is continuous at each point on its domain is

Question

$(a)\;2\qquad(b)\;\large\frac{1}{3}$$\qquad(c)\;\large\frac{2}{3}$$\qquad(d)\;-\large\frac{1}{3}$