Question

Given $f\left(x\right)=g\left(x\right).h\left(x\right)$. If $g\left(x\right)$ and $h\left(x\right)$ are continuous in a given interval then $f\left(x\right)$ would also be continuous in the same interval.

• A. True
• B. False

Answer 1

The correct option is A

True

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.