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Consider the function \( f:(-\infty, \infty) \rightarrow(-\infty, \infty) \) defined by
\( \mathrm{P} \) \( f(x)=\frac{x^{2}-a x+1}{x^{2}+a x+1} ; 0a2 \). (2008, 12M)
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Which of the following is true?
(a) \( f(x) \) is decreasing on \( (-1,1) \) and has a local minimum at \( x=1 \)
(b) \( f(x) \) is increasing on \( (-1,1) \) and has a local maximum at \( x=1 \)
(c) \( f(x) \) is increasing on \( (-1,1) \) but has neither a local maximum nor a local minimum at \( x=1 \)
(d) \( f(x) \) is decreasing on \( (-1,1) \) but has neither a local maximum nor a local minimum at \( x=1 \)
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