Question

Which of the following is false if both f(x) and g(x) are continuous?

(a) f(x)+g(x) is continuous

(b) f(x)-g(x)is continuous

(c) f(x)*g(x)is continuous

(d) \(\frac{f(x)}{g(x)}\) is continuous

This question was posed to me in final exam.

My query is from Continuity topic in section Complex Function Theory of Engineering Mathematics

Answer 1

The correct option is (d) \(\frac{f(x)}{g(x)}\) is continuous

To explain: For \(\frac{f(x)}{g(x)}\) to be continuous, the denominator needs to be greater than 0. If not, the function becomes infinity and cannot be determined, thereby becoming discontinuous.