Question

Barrett works at an ice cream shop. The function f(x) represents the amount of money PLEASE HELP!!!!!!!!!!!!!

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 + 4
g of x equals the square root of the quantity 3 x cubed

Answer 1

Answer:

$f(g(x))=6x^3+4$, it is the amount of money earned per number of hours of work, x

Step-by-step explanation:

Here we have two functions:

$f(x)=2x^2 +4$

This function represents the amount of money (the earning) per unit x

Then we have the function

$g(x)=\sqrt{3x^3}$

which represents the number of gallons of ice cream that Barrett makes per hour, where x is the number of hours he works.

Here we want to find the composite function

$f(g(x))$

which means that we use the output of $g(x)$ as input for $f(x)$. In this context, this means that the function $f(g(x))$ represents the amount of money earned per number of hours of work, x.

Substituting g(x) into the x of f(x), we find:

$f(g(x))=2(g(x))^2+4=2(\sqrt{3x^3})^2+4=2(3x^3)+4=6x^3+4$

Answer 2

Answer:

f(g(x)) = 6x^3 + 4 dollars/hour

Step-by-step explanation:

I took the test