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Question

If the function 'f' and 'g' are continuous at c then. Choose the incorrect alternative.


A

f + g is continuous at c

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B

f - g is continuous at c

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C

f.g is continuous at c

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D

is continuous at c

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Solution

The correct option is D

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 ϵδ 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,fg,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.


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