[tex]\begin{gathered} f(x)=|x^2-6| \\ \\ g(x)=\frac{1}{2}x+4 \end{gathered}[/tex]
[tex]f(-3)=|(-3)^2-6|=|9-6|=|3|=3[/tex][tex]g(0)=\frac{1}{2}(0)+4=0+4=4[/tex][tex]\begin{gathered} f(0)=|0^2-6|=|-6|=6 \\ \\ g(f(0))=\frac{1}{2}(f(0))+4=\frac{1}{2}(6)+4=3+4=7 \end{gathered}[/tex][tex]\begin{gathered} g(2)=\frac{1}{2}(2)+4=1+4=5 \\ \\ f(g(2))=|(g(2))^2-6|=|5^2-6|=|25-6|=|19|=19 \end{gathered}[/tex][tex]g(g(2))=\frac{1}{2}(g(2))+4=\frac{1}{2}(5)+4=\frac{5}{2}+4=\frac{5+8}{2}=\frac{13}{2}=6.5[/tex]
