Question

Barrett works at an ice cream shop. The function f(x) represents the amount of money Barrett earns per gallon of ice cream, where x is the number of gallons of ice cream he makes. The function g(x) represents the number of gallons of ice cream Barrett makes per hour, where x is the number of hours he works. Show all work to find f(g(x)), and explain what f(g(x)) represents.f(x) = 2x2 + 4g(x)= ^3x to the third power

Answer 1

As per given by the question,

There are given that the function ,

`\begin{gathered} f(x)=2x^2+4 \\ g(x)=\sqrt[]{3x^3} \end{gathered}`

Now,

For the finding of f(g(x)).

So,

Put the value of g(x) instead of x in f(x).

Then;

`\begin{gathered} f(x)=2x^2+4 \\ f(g(x)=\sqrt[]{3x^3})=2(\sqrt[]{3x^3})^2+4 \end{gathered}`

Then,

Solve the above equation f(g(x)),

`\begin{gathered} f(g(x)=\sqrt[]{3x^3})=2(\sqrt[]{3x^3})^2+4 \\ =2(3x^3)+4 \\ =6x^3+4 \end{gathered}`

Hence, the value of f(g(x)) is,

`f(g(x))=6x^3+4`