I solved this and think the range is: y>=3.Did I solve correctly?

Notice that
[tex]\begin{gathered} x^2\ge0,x\in\Re \\ \Rightarrow x^2+3\ge3,x\in\Re \\ \Rightarrow f(x)\ge3,x\in\Re \end{gathered}[/tex]Therefore, the range of the function is f(x)>=3, or [3,infinite)