A) \[2,\frac{7}{3},\frac{25}{11}\]
B) \[2,\frac{8}{3},\frac{24}{11}\]
C) \[2,\frac{7}{3},\frac{24}{11}\]
D) None of these
Correct Answer: C
Solution :
\[f(x)=\frac{1}{{{x}^{2}}-17x+66}\] \[\Rightarrow \] \[f(x)=\frac{1}{(x-6)(x-11)}\] Let, \[\frac{2}{x-2}=u,\] Then \[f\left( \frac{2}{x-2} \right)=f(u)=\frac{1}{(u-6)(u-11)}\] The function is discontinuous at the following points (i) \[x=2\] (ii) \[u=6\Rightarrow \frac{2}{x-2}=6\Rightarrow x=\frac{7}{3}\] (iii) \[u=11\Rightarrow \frac{2}{x-2}=11\Rightarrow x=\frac{24}{11}\]
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