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) = 2x^2 + 16 g(x) = sqrt 5x^3

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) = 2x^2 + 16 g(x) = sqrt 5x^3

supie · Answer

$f(x) = 2x^2 + 16 g(x) = \sqrt {5x^3}$?

Mercury · Answer

for the calculation: to calculate f(g(x)) simply take g(x) = sqrt(5x^3), substitute this for x inside the function f(x), and simplify

now, to think about what it means - notice how we just took x =  number of tickets sold per hour, and put it inside f(x), which represents the amount earned per ticket). the result is still f, so it's represents the amount earned, but notice how your final function is in terms of hours, not tickets.