A) {0, 2}
B) {0, 1, 2}
C) {0}
D) An empty set
Correct Answer: D
Solution :
[d] \[f(g)(x))=f(1-\left| x \right|)=-1+\left| \left| x \right|+1 \right|\] Let \[fog=y\] \[\therefore \,y=-1+\left| \left| x \right|+1 \right|\Rightarrow y=\left\{ \begin{matrix} x, & x\ge 0 \\ -x, & x<0 \\ \end{matrix} \right.\] LHL at \[(x=0)=\underset{x\to 0}{\mathop{\lim }}\,(-x)=0\] RHL at \[(x=0)=\underset{x\to 0}{\mathop{\lim }}\,(x)=0\] When \[x=0\], then \[y=0\] Hence, LHL at (x = 0)=RHL at (x = 0)= value of y at (x = 0) Hence y is continuous at x = 0 Clearly at all other point y continuous. Therefore, the set of all points where fog is discontinuous is an empty set.
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