If `f(x)={1/(1+e^((1,)/x)),x!=0 0,x=0,t h e nf(x)` is continuous as well as differentiable at `x=0` continuous but not differentiable at `x=0` differentiable but not continuous at `x=0` none of these

Explanation

To determine the continuity and differentiability of the function

\[
f(x) =
\begin{cases}
\frac{1}{1 + e^{\frac{1}{x}}}, & x \neq 0 \\
0, & x = 0
\end{cases}
...