Question

Please help verify if my answers are correct. So far I have f(-3)=3, g(0)=4, g(f(0))=7, don't know at all for f(g(2)), and g(g(2)) I have 6.5.

Answer 1

`\begin{gathered} f(x)=|x^2-6| \\ \\ g(x)=(1)/(2)x+4 \end{gathered}`

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