If the range of the function \( f(x)=\frac{x-1}{p-x^{2}+1} \) does not contain any values belong...

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If the range of the function \( f(x)=\frac{x-1}{p-x^{2}+1} \) does not contain any values belonging to the interval \( \left[-1, \frac{-1}{3}\right] \) then the true set of values of \( p \), is :
(a) \( (-\infty,-1) \)
(b) \( \left(-\infty, \frac{-1}{4}\right) \)
(c) \( (0, \infty) \)
(d) \( (-\infty, 0) \)
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