The given functions are:
[tex]\begin{gathered} f(x)=2x^2+4 \\ g(x)=\sqrt[]{3x^3} \end{gathered}[/tex]Replace x with g(x) in the function f(x):
[tex]f(g(x))=2(g(x))^2+4[/tex]Substitute the expression for g(x) into f(g(x)):
[tex]f(g(x))=2(\sqrt[]{3x^3})^2+4[/tex]
Cancel out the square root with the square:
[tex]\begin{gathered} \Rightarrow f(g(x))=2(3x^3)+4 \\ \Rightarrow f(g(x))=6x^3+4 \end{gathered}[/tex]Since f(x) represents the amount of money Barrett earns per gallon of ice cream and g(x) represents the number of gallons of ice cream Barrett makes per hour, it follows that the composite function f(g(x)) represents the amount of money Barrett earns per hour. The argument of the composite function (x) is the number of hours.
Answers:
[tex]f(g(x))=6x^3+4[/tex]f(g(x)) represents the amount of money Barrett earns selling gallons of ice cream per hour.