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
9(x)=√5x3

Answer 1

To find f(g(x)), substitute the function g(x) into the function f(x). f(g(x)) represents the amount of money Raul earns per hour based on the number of hours he works.

Step-by-step explanation:

To find f(g(x)), we need to substitute the function g(x) into the function f(x).

Given:
f(x) = 2x² + 169
g(x) = √5x³

Substitute g(x) into f(x):
f(g(x)) = 2(√5x³)² + 169

Simplify:
f(g(x)) = 2(5x³) + 169
f(g(x)) = 10x³ + 169

Therefore, f(g(x)) represents the amount of money Raul earns per hour based on the number of hours he works, where x is the number of hours.