The domain of a radical function is all the x-values for which the radicand is not negative. That means $\displaystyle{x}+{2}\ge{0}\usepackage{cmbright}\Huge\$ , so the domain is $\displaystyle{x}\ge-{2}\usepackage{cmbright}\Huge\$ . By definition, the square root symbol cannot have a negative value, so $\displaystyle\sqrt{{{x}+{2}}}\ge{0}\usepackage{cmbright}\Huge\$ . That means $\displaystyle-{7}+\sqrt{{{x}+{2}}}\ge-{7}\usepackage{cmbright}\Huge\$ . Therefore, the range is $\displaystyle{f{{\left({x}\right)}}}\ge-{7}\usepackage{cmbright}\Huge\$ .