A function is even if the following condition is satisfied: $h(-x) = h(x)$.
So, we substitute $-x$ into the function:
$$h(-x) = \frac{1}{-x} - 2(-x) = -\frac{1}{x} + 2x$$
We can see that $h(-x)$ is not equal to $h(x)$, so the function is not even.
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