Answer
$g(4)=-3$
$g(1)=-1.73$
$g\left (-\frac{1}{2} \right )=0$
$g(-1)=$ Not a real number.
Work Step by Step
The given function is
$g(x)=-\sqrt{2x+1}$
Plug $x=4$ into the function.
$g(4)=-\sqrt{2(4)+1}$
Simplify.
$g(4)=-\sqrt{8+1}$
$g(4)=-\sqrt{9}$
$g(4)=-\sqrt{3^2}$
$g(4)=-3$
Plug $x=1$ into the function.
$g(1)=-\sqrt{2(1)+1}$
Simplify.
$g(1)=-\sqrt{2+1}$
$g(1)=-\sqrt{3}$
Round to two decimal places.
$g(1)=-1.73$
Plug $x=-\frac{1}{2}$ into the function.
$g\left (-\frac{1}{2} \right )=-\sqrt{2\left (-\frac{1}{2} \right )+1}$
Simplify.
$g\left (-\frac{1}{2} \right )=-\sqrt{-1+1}$
$g\left (-\frac{1}{2} \right )=-\sqrt{0}$
$g\left (-\frac{1}{2} \right )=-0$
$g\left (-\frac{1}{2} \right )=0$
Plug $x=-1$ into the function.
$g(-1)=-\sqrt{2(-1)+1}$
Simplify.
$g(-1)=-\sqrt{-2+1}$
$g(-1)=-\sqrt{-1}$
Not a real number.