A) 1
B) 2
C) 3
D) none of these
Correct Answer: A
Solution :
[a] \[f(x)=\left\{ \begin{matrix} x+2, \\ -{{x}^{2}}-2, \\ x, \\ \end{matrix} \right.\begin{matrix} x<0 \\ \,\,\,\,0\le x<1 \\ x\ge 1 \\ \end{matrix}\] \[\therefore \,\,\,\,\left| f(x) \right|=\left\{ \begin{matrix} -x-2, \\ x+2, \\ {{x}^{2}}+2, \\ x, \\ \end{matrix} \right.\,\,\,\begin{matrix} x<-2 \\ \,\,\,\,-2\le x<0 \\ \,\,\,0\le x<1 \\ x\ge 1 \\ \end{matrix}\] It is discontinuous at x=1. Therefore, number of discontinuity is 1.
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