F(x) = the square root of x+2
g(x)=x cubed -2

what is (g open circle f) (x)
and the domain?

now. the domain, will be constrained, by the issue that, an EVEN root, cannot have a negative radicand, so... theh square root, cannot have a negative amount inside.... so, "x" can have any real values, so long it doesn't make x+2 a negative number, now, 0 is ok, but less than that, no dice

let's see what makes x+2 to zero then

x+2 = 0 => x = -2

so if we set x = -2, we end  up with (-2)+2 = 0, and that's ok for the domain

now, if we go below -2 though, like say (-3) + 2, then we end up with -1
if we make it -4, -5, -100 and so on, we end up with a negative radicand

so.... the domain will be    or x > -3