0≤x²≤2 how does one do this?

First, you may want to visualize what is happening here.

Graph y=x^2. The graph is that of a parabola that opens up. Draw a horizontal line through y=2 and another through y=0 (which is really the x-axis). Put dots where the curve intersects these lines.

Draw vertical lines through the two dots where the curve intersects the horiz. line y=2. Note where these two lines intersect the x-axis. From your graph, you can approximate the domain: it is roughly [-1.414, 1.414], or [-sqrt (2), - sqrt (2).

You could also take the sqrt of all 3 terms in the given inequality.

Then sqrt (0) ≤ sqrt (x²) ≤ sqrt (2), which is equivalent to 0 ≤ |x| ≤sqrt (2).

This allows for negative x in [-sqrt (2),).

The domain of this function is [-sqrt (2), + sqrt (2) ].

The range is 0 ≤ y ≤ 2.