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As $x$ increases:
$\sqrt{4x^4-4x^2+2} = \sqrt{(2x^2-1)^2+1}$ decreases if $x \in [0,\frac12\sqrt2]$ and increases if $x \in [\frac12\sqrt2,-\infty)$.
Symmetrically $\sqrt{4x^4-4x^2+2}$ decreases if $x \in (-\infty,-\frac12\sqrt2]$ and increases if $x \in [-\frac12\sqrt2,0]$.
Therefore $\sq...