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

Answer 1

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) = $2x^2 + 16$

g(x) = $\sqrt{(5x^3)}$

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)  = $2x^2 + 16$

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

The square root and power 2 cancel each other

f(g(x))  = $2(5x^3 ) +16$

f(g(x)) = $10x^3 +16$

So at x hours

Raul earns $10x^3 +16$

For example lets assume Raul works for 5 hours, then the amount he earns will be

f(g(x)) = $10(5)^3 +16$

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) = $\sqrt{(5(5)^3)}$

g(x) = $\sqrt{625}$

g(x) = 25

Substituting in f(x)

f(g(x)) = f(25)

f(25)  = $2(25)^2 + 16$

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