if A={x|x is an integer and -3≤ x²+1 <2}

Answer 1

-3 ≤ x²+1 < 2 means that you are looking for the portion of the "x²+1" graph where the y-values are less than 2 and greater than -3. Visually, we can show this on the graph as the grey shaded portion between the y = 2 and y = -3 lines like this:

So the only place on the "x²+1" graph is in that shaded portion is between x = -1 and x = 1. But when x = -1 and x = 1 the y values of "x²+1" equal 2 and we need to be < 2. So the only INTEGER that works is x = 0