Question

If $f\left(x\right)=\frac{1}{x^2-17x+66}$ then $f\left(\frac{2}{x-2}\right)$ is discontinuous at $x$ is equal to

• 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. $2,6,11$

Answer 1

The correct option is C $2,\frac{7}{3},\frac{24}{11}$

$f\left(x\right)=\frac{1}{x^2-17x+66}$

$=\frac{1}{(x-6)(x-11)}$

$⟹x\ne 6,11$

$f\left(\frac{2}{x-2}\right)$ is discontinuous at $x=2$ and $\frac{2}{x-2}=6,11$

$\frac{x-2}{2}=\frac{1}{6},\frac{1}{11}$

$⟹x=\frac{7}{3},\frac{24}{11}$