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BabaBlast [244]
3 years ago
6

Barrett works at an ice cream shop. The function f(x) represents the amount of money Barrett earns per gallon of ice cream, wher

e 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. Show all work to find f(g(x)), and explain what f(g(x)) represents.
f(x) = 2x^{2} + 4
g(x) = \sqrt{3x^{3}
Mathematics
1 answer:
Sliva [168]3 years ago
4 0

The value of f(g(x)) is 6x^{3} +4

Explanation:

The function f(x) is given by

f(x)=2x^{2} +4

The function g(x) is given by

g(x)=\sqrt{3x^{3} }

To determine the value of f(g(x)), let us first substitute the value of g(x).

Thus, we get,

f(g(x))=f(\sqrt{3x^{3} } )

Now, substituting for x=\sqrt{3x^{3} } in the function f(x), we get,

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

Simplifying, the expression, we get,

f(g(x))=2({3x^{3} } )+4

Multiplying the term within the bracket, we have,

f(g(x))=6x^{3} +4

Thus, the value of f(g(x)) is 6x^{3} +4

Hence, the value of f(g(x)) represents the total amount of money that Barrett earns for working x hours.

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