#### Answer

We can let $\delta = 0.2$

#### Work Step by Step

On the graph, we can see that values between approximately 0.7 and 1.2 will yield squares between 0.5 and 1.5
$\vert 1-0.7 \vert = 0.3$ and $\vert 1 - 1.2 \vert = 0.2$
Therefore, we can let $\delta = 0.2$
If $\vert 1-x \vert \lt 0.2$, then $\vert x^2 - 1 \vert \lt \frac{1}{2}$