Answer
$|1-2x^{2}|=(1-2x^{2}), x€(-\frac{1}{\sqrt 2},\frac{1}{\sqrt 2})$
And
$|1-2x^{2}|=-(1-2x^{2}), x€(-∞,-\frac{1}{\sqrt 2})∪x€( \frac{1}{\sqrt 2},∞)$
Work Step by Step
For $x =0 \ or \ x> 0,| x| = x$
For $x< 0,| x| = -x$
Now, apply above definition for the expression $|1-2x^{2}|$.
$|1-2x^{2}|>0$ if $x€(-\frac{1}{\sqrt 2},\frac{1}{\sqrt 2})$
And
$|1-2x^{2}|<0$ if $x€(-∞,-\frac{1}{\sqrt 2})$$∪$$x€( \frac{1}{\sqrt 2},∞)$
Therefore,
$|1-2x^{2}|=(1-2x^{2}),x€(-\frac{1}{\sqrt 2},\frac{1}{\sqrt 2})$
And
$|1-2x^{2}|=-(1-2x^{2}), x€(-∞,-\frac{1}{\sqrt 2})∪x€( \frac{1}{\sqrt 2},∞)$
