Calculate the variance from a function of normal random variable

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I am new to the topic that I found difficulty for the question:

Given the function $g(x) = e^{-X}$, $X \sim N(0,1)$, calculate the variance of $g(x)$.

I know the answer is $e(e-1)$. But I don't know how to get that. Can anyone help?

In additions, would anyone provide me a book that may explore this area?

Thanks.