The domain of a radical function is all the x-values for which the radicand is not negative. That means $\displaystyle{x}-{3}\ge{0}\usepackage{cmbright}\Huge\$ , so the domain is $\displaystyle{x}\ge{3}\usepackage{cmbright}\Huge\$ . By definition, the square root symbol cannot have a negative value, so $\displaystyle\sqrt{{{x}-{3}}}\ge{0}\usepackage{cmbright}\Huge\$ . If you multiply both sides by $\displaystyle-{1}\usepackage{cmbright}\Huge\$ you get $\displaystyle-\sqrt{{{x}-{3}}}\le{0}\usepackage{cmbright}\Huge\$ . That means $\displaystyle{4}-\sqrt{{{x}-{3}}}\le{4}\usepackage{cmbright}\Huge\$ . Therefore, the range is $\displaystyle{f{{\left({x}\right)}}}\le{4}\usepackage{cmbright}\Huge\$ .