Question of continuity

Q1-

A: if f(x) is discontinous at a point c and g(x) is continous at c and f(x).g(x) is continous at c then f(x) must be 0 at point c.

B: if f(x) and g(x) are two continous function in their domain then f(x).g(x) must be continous function and if atleast one of the fn is discontinous then f(x).g(x) may be continous.

a) A is true R is true ,R explains A.

b) A is true R is true ,R not explain A.

c) A is false R is true.

d) A is true R is false.

Q2- (a basic question)

A- a function f(x)=1/1-x is a continous function.

R-a continous function is that which is continous in its domain with no breaks and hence in the function f(x)=1/1-x x=1 is not in the domain of this function.however f(1) does not exit.

a) A is true R is true ,R explains A.

b) A is true R is true ,R not explain A.

c) A is false R is true.

d) A is true R is false.