Question

If $f\left(x\right)$ is continuous at $x=c$ and $g\left(x\right)$ is continuous at $x=f\left(c\right)$ then which of the following is/are continuous at $x=c$?

• A. $\left(f\right(x)-g(x\left)\right)\ast f\left(x\right)$
• B. $f\left(g\right(x\left)\right)$
• C. $f\left(f\right(x\left)\right)$
• D. None

Answer 1

The correct option is D None

Given that the function $f$ is continuous at $x=c$

Given that the function $g$ is continuous at $x=f\left(c\right)$

therefore $g\left(f\right(x\left)\right)$ is continuous at $x=c$

Therefore the correct option is $D$