fog=f(g(x))=f(1−|x|) =−1+|1−|x|−2| =−1+|−|x|−1|=−1+∥x|+1| Let fog=y ∴y=−1+∥x|+1| ⇒y={
−1+x+1,
x≥0
−1−x+1,
x<0
⇒y={
x,
x≥0
−x,
x<0
LHL at (x=0)=
lim
x→0
(−x)=0 RHL at (x=0)=
lim
x→0
(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.