Discover how IDNLearn.com can help you learn and grow with its extensive Q&A platform. Discover thorough and trustworthy answers from our community of knowledgeable professionals, tailored to meet your specific needs.

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 using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Your questions deserve reliable answers. Thanks for visiting IDNLearn.com, and see you again soon for more helpful information.