Q102 / 160 · TS EAMCET 2018 (04 May Shift 2) · Mathematics

The number of points at which the function $f(x)=\frac{\sqrt{11+|x|-6 \sqrt{2+|x|}}}{6-2 \sqrt{2+|x|}}$ is discontinuous in $(-\infty, \infty)$ is

  • A
    1
  • B
    0
  • Correct answer
    C
    2
  • D
    3

Solution

$f(x)=\sqrt{\frac{11+|x|-6 \sqrt{2+|x|}}{6-2 \sqrt{2+|x|}}}$ This function will be discontinuous where function is undefined. So, it is undefined, if $\frac{11+|x|-6 \sqrt{2+|x|}}{6-2 \sqrt{2+|x|}} < 0$ and $6-2 \sqrt{2+|x|}=0$ and $2+|x| < 0$ Now, $2+|x| < 0 \Rightarrow|x| < -2$ Not possible. $$ \begin{aligned} & \text { Again } 6-2 \sqrt{2+|x|}=0 \\ & \Rightarrow \quad-2 \sqrt{2+|x|}=-6 \\ & \Rightarrow \quad \sqrt{2+|x|}=3 \Rightarrow 2+|x|=9 \\ & \Rightarrow \quad|x|=7 \quad \Rightarrow \quad x= \pm 7 \\ & \end{aligned} $$ Hence, numbers of points is 2 .

Hence, the correct answer is option: 'C'.

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