The domain for that function is all real numbers. As the function continues to grow higher, the x values will also continue to grow without end. The range is found when x = 0. When x = 0, y = 3, so the range for the function is [tex]y \geq 3[/tex]. To find the inverse of the function, switch the x and y coordinates and solve for the new y. [tex]x=y^2+3[/tex]. Solving that for y gives us [tex]y= \sqrt{x-3} [/tex]. The domain of the function is found where [tex]x-3 \geq 0[/tex] since we cannot have a negative number under the square root. That means that the domain is [tex]x \geq 3[/tex] and the range will be all real numbers. If you notice (and it is always the case), the domain of the function is the range of its inverse, and the range of the function is the domain of its inverse.
