Answer:
See below
Step-by-step explanation:
This is a piecewise-defined function:
[tex]x=-1; x=1; x=4[/tex]
For [tex]h(-1):[/tex]
[tex]$h(-1)=-\frac{1}{2}x -2 \implies h(-1)=-\frac{1}{2}(-1) -2 \implies h(-1)=\frac{1}{2}-2$[/tex]
[tex]$h(-1)=\frac{1}{2} -\frac{4}{2} \implies \large\boxed{h(-1)=-\frac{3}{2}}$[/tex]
For [tex]h(1):[/tex]
[tex]$h(1)=-(x+1)^2 + 3 \implies h(1)=-(1+1)^2+3 \implies h(1)=-4+3 \implies \large\boxed{h(1)=-1}$[/tex]
For [tex]h(4):[/tex]
[tex]\large\boxed{h(4)=1}[/tex]
