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

Apr 14, 2015

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

(1)
$f \left(x\right) = x + 7$ has a range where you put in any value $x \le 4$

So range of $f \left(x\right) \le 4 + 7 = 11 \to$
 -oo < f(x)<=11

(2)
If $x > 4$ then ${x}^{2} > {4}^{2} \to {x}^{2} > 16$

So the range is $16 < f \left(x\right) < \infty$