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) $u=6\Rightarrow \frac{2}{x-2}=6\Rightarrow x=\frac{7}{3}<br>$
(iii) $u=11\Rightarrow \frac{2}{x-2}=11\Rightarrow x=\frac{24}{11}$