Hi Felicia!
[tex]\rm f(x)=2x^2+5\sqrt{x+2}[/tex]
Remember that your square root function can only calculate positive values and zero. We can't put a negative under a square root.
This means that the "stuff" under the root must be greater than or equal to zero (positive).
[tex]\rm x+2\ge0[/tex]
Solve for x in this equation, subtracting 2 from each side,
[tex]\rm x\ge -2[/tex]
This is our domain, all x values -2 or larger.
Hope that helps! :)
