Given:
[tex]g(x)=\begin{cases}\frac{1}{2}x^2-5,x\ne2 \\ 4,x=2\end{cases}[/tex]To find g(-4), we will take the function when x is not equal to 2, therefore,
[tex]\begin{gathered} g(-4)=\frac{1}{2}(-4)^2-5 \\ =\frac{1}{2}\lbrack16\rbrack-5 \\ =8-5 \\ =3 \end{gathered}[/tex]Therefore, g( - 4) = 3
To find g(2),
The value of function at x = 2 is 4 so g(2)=4
To find g( 5):
[tex]\begin{gathered} g(5)=\frac{1}{2}\lbrack5^2\rbrack-5 \\ =\frac{25}{2}-5 \\ =\frac{25-10}{2} \\ =\frac{15}{2} \\ =7.5 \end{gathered}[/tex]Therefore, g(5) = 7.5