If the function \( f(x)=\frac{2 x-\sin ^{-1} x}{2 x+\tan ^{-1} x} \...

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If the function \( f(x)=\frac{2 x-\sin ^{-1} x}{2 x+\tan ^{-1} x} \) is continuous at each point of its domain, then the value of \( f(0) \) is
(a) 2
(b) \( \frac{1}{3} \)
(c) \( -\frac{1}{3} \)
(d) \( \frac{2}{3} \)
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