Question

If h(x) = f(x).g(x) is continuous in an interval then the functions f(x) and g(x) will also be continuous in the same interval.

• A. True
• B. False

Answer 1

The correct option is B

False

This can be easily imagined by taking a sample function to disprove it.

Let h(x) = 1. This function is continuous throughout the domain $\to$ R

$h\left(x\right)=1=\frac{1}{x}.x=f\left(x\right).g\left(x\right)$

where $f\left(x\right)=\frac{1}{x},g\left(x\right)=x$

f(x) is a function discontinuous at x = 0, which disproves the given statement.

Hence the statement is false.