Answer
a-No
b-No
c-No
d-No
e-Yes
f-Yes
g-Yes
Work Step by Step
a-As to check continuity , left hand limit should be equal to right hand limit. But in this case ,L.H.L of f(x) is 0 and R.H.L is 1.
b-As to check continuity , left hand limit should be equal to right hand limit. But in this case ,L.H.L of g(x) is 1 and R.H.L is 0.
c-As to check continuity , left hand limit should be equal to right hand limit. But in this case ,L.H.L of f(-x) is 1 and R.H.L is 0.
d-As to check continuity , left hand limit should be equal to right hand limit. But in this case ,L.H.L of |g(x)| is 1 and R.H.L is 0.
e-As to check continuity , left hand limit should be equal to right hand limit. But in this case ,L.H.L of f(x)g(x) is equal to R.H.L.
f-As to check continuity , left hand limit should be equal to right hand limit. But in this case ,L.H.L of g(f(x)) is equal to R.H.L.
g-As to check continuity , left hand limit should be equal to right hand limit. But in this case ,L.H.L of (f(x)+g(x)) is equal to R.H.L.
