Question

Raul works at a movie theatre. The function f(x) represents the amount of money Raul earns per ticket, where x is the number of tickets he sells. The function g(x) represents the number of tickets Raul sells 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) = 2x2 + 16
g of x equals the square root of the quantity 5 x cubed

Answer 1

anyone? o.O

Answer 2

helloooo?

Answer 3

nvmmmm

Answer 4

So I'm assuming
\[g(x)=\sqrt{5x ^{3}}\]\[f(x)=2x ^{2}+16\]
Recall what the meaning of f(x) is for any function. f(x) simply defines the input being plugged into the equation. In this case, f(x) is determined by the input plugged into g(x). Whatever the output of g(x) is used as the input of f(x). That is what f(g(x)) means. To find f(g(x)), all you have to do is plug in g(x) for x. This would mean that\[f(g(x))=2(\sqrt{5x ^{3}})^{2}+16\]Then just solve for that.
As for what f(g(x)) means, it represents the total amount of money earned given the number of hours worked at the movie theater, and g(x) returns the number of tickets that have been sold.