Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

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

Sagot :

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

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 = [tex]f(x) = 2x^{2} + 4[/tex]

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

we are to find the composite function [tex]f(g(x))[/tex]

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

[tex]f(g(x)) = 2(\sqrt{3x^{3} } )^{2} + 4\\\\= 2(3x^{3} ) + 4\\= 6 x^{3} + 4[/tex]

To learn  more about composite function from given link

https://brainly.com/question/14865610

#SPJ4

Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.