Question

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

• A. f + g is continuous at c
• B. f - g is continuous at c
• C. f.g is continuous at c
• D. is continuous at c

Answer 1

The correct option is D

is continuous at c

$\frac{f}{g}$ is continuous only when $g\left(c\right)\ne 0$ which is a necessary condition. i.e., $\frac{f}{g}$ is discontinuous at c if g(c) = 0.

The proof of the properties are proved using $ϵ-\delta$ method which will be introduced in higher mathematics.

Here we assume very small neighborhood $\delta$ and $ϵ$ for the values x and functions f, g. then we see if the functions $f+g,f-g,f.g,\frac{f}{g}$ also comes within a small neighborhood in terms of $ϵ$. If it comes like that then the resultant function is also continuous.