Question

Given f(x) = g(x).h(x). If g(x) and h(x) are continuous in a given interval then f(x) will be in the same interval.

• A. continuous
• B. discontinuous
• C. constant
• D. increasing

Answer 1

The correct option is A continuous

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.