Question

If $ f(x)=\frac{1}{{{x}^{2}}-17x+66}, $ then for what values of $ x,f\left( \frac{2}{x-2} \right) $ is discontinuous?

• 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

Answer 1

Answer: (C)

$ 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} $