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Samantha works at a bakery. The function f(x) = 7x2 − 3 represents the amount of money Samantha earns per cookie, where x is the number of cookies she makes. The function g of x equals square root of quantity 4 times x to the fifth power end quantity represents the number of cookies Samantha bakes per hour, where x is the number of hours she works. Find f(g(x)), and explain what it represents.

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MrRoyal

The equation of the composite function f(g(x)) is f(g(x)) = 28x^5 - 3 and the interpretation is the amount of money earned when Samantha works for x hours

How to determine the composite function f(g(x))?

The functions are given as:

f(x) = 7x^2 - 3

g(x) = √4x^5

To determine the composite function f(g(x)), we have:

f(x) = 7x^2 - 3

Substitute g(x) for x in the above equation f(x) = 7x^2 - 3

f(g(x)) = 7(g(x)^2 - 3

Substitute √4x^5 for g(x) in the above equation f(g(x)) = 7(g(x)^2 - 3

f(g(x)) = 7(√4x^5)^2 - 3

Expand the exponent

f(g(x)) = 7 * 4x^5 - 3

Evaluate the product

f(g(x)) = 28x^5 - 3

Hence, the equation of the composite function f(g(x)) is f(g(x)) = 28x^5 - 3

And the interpretation is the amount of money earned when Samantha works for x hours

Read more about composite functions at:

https://brainly.com/question/13502804

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