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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:
f(g(x))=
Step-by-step explanation:
Given:
f(x) =
g(x) =
f(x) represents the amount of money Raul earns per ticket
x is the number of tickets he sells
g(x) represents the number of tickets Raul sells per hour
To find:
f(g(x)) = ?
Solution:
f(g(x)) represent the amount Raul earns by selling tickets for x hours
We know,
f(x) =
f(g(x)) =
The square root and power 2 cancel each other
f(g(x)) =
f(g(x)) =
So at x hours
Raul earns
For example lets assume Raul works for 5 hours, then the amount he earns will be
f(g(x)) =
f(g(x)) = 10(125) +16
f(g(x)) = 1250 +16
f(g(x)) = 1266
You can also find the amount Raul earns by
g(x) =
g(x) =
g(x) = 25
Substituting in f(x)
f(g(x)) = f(25)
f(25) =
f(25) = 2(625) +16
f(25) = 1250 + 16
f(25) = 1266
so Raul will be earning 1266 if he sells tickets for 5 hours