Question

Barrett works at an ice cream shop. the function f(x) represents the amount of money in dollars 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. f(x) = 2x2 4 g(x) = the square root of three times x cubed find f(g(x)). f of g of x equals the square root of the quantity 6 times x to the fifth power plus 4 dollars over hour f of g of x equals the square root of the quantity 6 times x to the fifth power plus 4 gallons over hour f(g(x)) = 6x3 4 gallons over hour f(g(x)) = 6x3 4 dollars over hour

Answer 1

Amount of money earned per number of hours of work =  $f(g(x)) = 6x^{3} + 4$

What is a composite function?

• A composite function is generally a function that is written inside another function.
• Composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”.

To evaluate a composite function f(g(x)) at some x = a, first compute g(a) by substituting x = a in the function g(x). Then substitute g(a) into the function f(x) by substituting x = g(a). In the same way, we can calculate g(f(a)) as well.

Required calculation -

Amount of money (the earning) per unit x = $f(x) = 2x^{2} + 4$

Number of gallons of ice cream that Barrett makes per hour, where x is the number of hours he works = $g(x) = \sqrt{3x^{3}}$

we are to find the composite function $f(g(x))$

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

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

To learn  more about composite function from given link

https://brainly.com/question/14865610

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