Find the Domain of

I can do this Question using graphs. I need help in doing it without graphs ... some help please

Find the Domain of

$\displaystyle -1 <= [2x^2 - 3] <= 1$

$\displaystyle -1 <= (2x^2 - 3) < 2$

$\displaystyle 1 <= x^2 < \frac{5}{2}$

Why?

$\displaystyle |x| >= 1$ and $\displaystyle |x| < \sqrt{\frac{5}{2}}$

$\displaystyle x \in (-\sqrt{\frac{5}{2}},-1]\cup[1,\sqrt{\frac{5}{2}})$

but the answer is

$\displaystyle x \in [-\sqrt{\frac{5}{2}},-1]\cup[1,\sqrt{\frac{5}{2}}]$

Why is the 5/2 terms included?