If the function 'f' and 'g' are continuous at c then. Choose the incorrect alternative.
is continuous at c
fg is continuous only when g(c)≠0 which is a necessary condition. i.e., fg is discontinuous at c if g(c) = 0.
The proof of the properties are proved using ϵ−δ method which will be introduced in higher mathematics.
Here we assume very small neighborhood δ and ϵ for the values x and functions f, g. then we see if the functions f+g,f−g,f.g,fg also comes within a small neighborhood in terms of ϵ. If it comes like that then the resultant function is also continuous.