Test Function/Examples/Exponential of One over x Squared minus One

Theorem
Let $\phi : \R \to \R$ be a Definition:Real Function such that:


 * $\map \phi x = \begin{cases}

\ds \map \exp {\frac 1 {x^2 - 1}} & : \size x < 1 \\ 0 & : \size x \ge 1 \end{cases}$

Then $\phi$ is a test function.