A) \[(2,\infty )\]
B) \[(-\infty ,3)\]
C) \[(-\infty ,-3)\cup (3,\infty )\]
D) none of these
Correct Answer: C
Solution :
[c] \[f(x)=\left\{ \begin{matrix} {{x}^{2}}-ax+3,\,\,\, \\ 2-x,\, \\ \end{matrix} \right.\begin{matrix} x\,\,is\,\,rational \\ x\,\,\text{is}\,\,\text{irrational} \\ \end{matrix}\] It is continuous when \[{{x}^{2}}-ax+3=2-x\]or \[{{x}^{2}}-(a-1)x+1=0\] Which must have two distinct roots for \[{{(a-1)}^{2}}-4>0\] Or \[(a-1-2)(a-1+2)>0\] Or \[a\in (-\infty ,-1)\cup (3,\infty )\]
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