Continuous Real Function on Closed Interval/Examples/Reciprocal of 1 + e to the Reciprocal of x

Examples of Continuous Real Functions on Closed Intervals
Consider the real function $f$ defined as:
 * $f := \begin {cases} \dfrac 1 {1 + e^{1 / x} } & : x \ne 0 \\ 0 & : x = 0 \end {cases}$

Then $f$ is continuous on the closed interval $\closedint 0 1$.