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Sonia works at a bakery. The function f(x) represents the amount of money in dollars Sonia earns per loaf, where x is the number of loaves she makes. The function g(x) represents the number of bread loaves Sonia bakes per hour, where x is the number of hours she works.

f(x) = 9x2 + 1

g(x) = the square root of two times x cubed

Find f(g(x)).

f(g(x)) = 18x3 + 1 dollars over hour
f(g(x)) = 18x3 + 1 loaves over hour
f of g of x equals the square root of the quantity 18 times x to the fifth power plus 1 loaf per hour
f of g of x equals the square root of the quantity 18 times x to the fifth power plus 1 dollar over an hour


Sagot :

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Step-by-step explanation:

The function f(g(x)) is an illustration of a composite function of f(x) and g(x). The composite function f(g(x)) is [tex]f(g(x)) = 18x^3 + 1[/tex]

Given that:

[tex]f(x) = 9x^2 + 1[/tex]

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

f(g(x)) is calculated as follows:

[tex]f(x) = 9x^2 + 1[/tex]

Substitute g(x) for x

[tex]f(g(x)) = 9(g(x)^2) + 1[/tex]

Substitute [tex]g(x) = \sqrt{2x^3}[/tex]

[tex]f(g(x)) = 9((\sqrt{2x^3})^2) + 1[/tex]

[tex]f(g(x)) = 9(2x^3) + 1[/tex]

Open bracket

[tex]f(g(x)) = 18x^3 + 1[/tex]

Hence, composite function f(g(x)) is [tex]f(g(x)) = 18x^3 + 1[/tex]

Read more about composite functions at:

https://brainly.com/question/8776301