Question

The point(s) of discontinuity of the function $f\left(x\right)=\frac{1}{x^2-3\left|x\right|+2}$ is/are

• A. $x=\pm 3$
• B. $x=\pm 2$
• C. $x=\pm 1$
• D. $x=0$

Answer 1

Answer: (B), (C)

$x=\pm 1$

$f\left(x\right)=\frac{1}{x^2-3\left|x\right|+2}$
$f\left(x\right)$ is discontinuous when $x^2-3\left|x\right|+2=0$
$\Rightarrow {\left|x\right|}^2-3\left|x\right|+2=0$
$\Rightarrow (\left|x\right|-1)(\left|x\right|-2)=0$
$\Rightarrow \left|x\right|=1,2$
$\Rightarrow x=\pm 1,\pm 2$ are points of discontinuity for $f\left(x\right).$