Question

How do you find the domain of `F(x)=x+7` if `x<=4` and `x^2` if x > 4?

Answer 1

You have allready given the domains by giving the limits on `x`
Probably you meant range .

(1)
`f(x)=x+7` has a range where you put in any value `x<=4`

So range of `f(x)<=4+7=11->`
# -oo < f(x)<=11#

(2)
If `x>4` then `x^2>4^2->x^2>16`

So the range is `16 < f(x) < oo`