Domain: Possible x values.
There's nothing like a fraction bar (can't divide by 0) or a square root (no square roots of negative numbers), so there's nothing that makes certain values of x not work.
Domain: - Infinity < x < + Infinity
Range: Possible y values
The smallest x^2 can ever be is 0, so the smallest 1 + 2x^2 can ever be is 1.
Range: 1 <= y < + Infinity