Question

Consider the following functions:
1. $f\left(x\right)=e^x$, where $x>0$
2. $g\left(x\right)=|x-3|$
Which of the above functions is/are continuous?

• A. 1 only
• B. 2 only
• C. Both 1 and 2
• D. Neither 1 nor 2

Answer 1

Answer: (C)

Both 1 and 2

$1.f\left(x\right)=e^x$

$\underset{x\to a}{lim}f\left(x\right)=\underset{x\to a}{lim}{e}^x=e^a$

$f\left(a\right)=e^a=\underset{x\to a}{lim}f\left(x\right)$

$\therefore$It is continuous

$2.g\left(x\right)=|x-3|$

$p\left(x\right)=(x-3)\&q\left(x\right)\left|x\right|$ both are continuous

$\Rightarrow |x-3|$ is also continuous $\left(p\right(q\left(x\right))$