Answer:
[tex]g(4f(2))=294[/tex]
Step-by-step explanation:
from
[tex]f(x)=\frac{1}{x} +1[/tex]
[tex]g(x)=x(x+1)^2[/tex]
then,
[tex]f(2)=\frac{1}{2} +1[/tex]
[tex]f(2)=\frac{3}{2}[/tex]
[tex]4f(2)=4(\frac{3}{2} )=6[/tex]
again,
[tex]g(4f(2))=4f(2)(4f(2)+1)^2[/tex]
but [tex]4f(2)=6[/tex]
[tex]g(4f(2))=6(6+1)^2=6(7)^2=6(49)[/tex]
Therefore [tex]g(4f(2))=294[/tex]
