If \( f: D \rightarrow R, f(x)=\frac{x^{2}+b x+c}{x^{2}+b_{1} x+c_{1}} \), where \( \alpha, \beta \) are the roots of the equation \( x^{2}+b x+c=0 \) and \( a_{1}, \beta_{1} \) are the roots of \( x^{2}+b_{1} x+c_{1}=0 \). Now, answer the following questions for \( f(x) \). A combination of graphical and analytical approach may be helpful in solving these problems. (If \( \alpha_{1} \) and \( \beta_{1} \) are reah then \( f(x) \) has vertical asymptote at \( \left.x=\alpha_{1}, \beta_{1}\right) \). Then,
If \( \alpha_{1}\alpha\beta_{1}\beta \), then
(a) \( f(x) \) is increasing in \( \left(\alpha_{1}, \beta_{1}\right) \)
(b) \( f(x) \) is decreasing in \( (\alpha, \beta) \)
(c) \( f(x) \) is decreasing in \( \left(\beta_{1}, \beta\right) \)
(d) \( f(x) \) is decreasing in \( (-\infty, \alpha) \)
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