The function f(x) = e|x| is
(a) continuous everywhere on R
(b) not continuous at x = 0
(c) Differentiable everywhere on R
(d) not differentiable at x = 0
(e) continuous and differentiable on R
Choose the most appropriate answer from the options given below :
Answer & explanation
Correct answer: option 3
$f(x) = e^{|x|}$
$f(x)=e^{|x|}= \begin{cases}e^x & x \geq 0 \\ e^{-x} & x<0\end{cases}$
$\left.\begin{array}{l}f(0)=1 \\ \lim\limits_{x \rightarrow 0} f(x)=1\end{array}\right\} \begin{array}{r}\text { continuous }\end{array}$
$f'(x) = \begin{cases}e^x & x \geq 0 \\ -e^{-x} & x<0\end{cases}$
$\left.\begin{array}{l}f'(0)=1 \\ \lim\limits_{x \rightarrow 0} f'(x)=-1\end{array}\right\} \begin{array}{r}\text { not differentiable at x =0}\end{array}$
Option: 3