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( and explain what f(g(x)) represents.

10x +16 that is the answer

f(g(x)) = 10x³ + 16

f(g(x)) is the amount of money Raul earns when he works x hours

Step-by-step explanation:

f(g(x)) = 10x³ + 16

f(g(x)) is the amount of money Raul earns when he works x hours

Step-by-step explanation:

* Lets explain the composite functions

- A composite function is created when one function is substituted into

 another function.

- Ex: f(g(x)) is the composite function that is formed when g(x) is

  substituted for x in f(x)

* Lets solve the problem

- 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

∵ f(x) = 2x² + 16

∵ g(x) = √(5x³)

- To find f(g(x)) substitute g(x) for x in f(x)

∴ f(g(x)) = f(√(5x³))

∴ f(g(x)) = 2[√(5x³)]² + 16

∵ [√(5x³)]² = 5x³ ⇒ power 2 canceled √

∴ f(g(x)) = 2(5x³) + 16 ⇒ simplify

∴ f(g(x)) = 10x³ + 16

∵ f(x) is the money Raul earns per ticket, where x is the number

  of tickets

∵ g(x) is the number of tickets Raul sells per hour, where x is the

   number of hours he works

∴ f(g(x)) is the amount of money Raul earns when he works x hours

* Lets explain that by numbers

- If Raul works 5 hours

∴ g(5) = √[5(5)³] = 25

∴ The number of tickets in 5 hours = 25 tickets

∴ f(25) = 2(25)² + 16

∴ f(25) = 2(625) + 16 = 1250 + 16 = 1266

∴ Raul earns $1266 in 5 hours

- If you substitute x by 5 in f(g(x)) you will have the same answer

∵ f(g(5)) = 10(5)³ + 16 = 1250 + 16 = 1266

f(g(x)) represents:

The amount of money Raul earns f, depends of number of tickets he sells g, and that depends on the number of hours he works x.

Step-by-step explanation:

Given that the function f(x) represents the amount of money Raul earns per ticket, and 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.

Now,

The amount of money Raul earns per ticket is a function of the number of ticket he sells.

Likewise, the number of tickets he sells is a function of the number of hours he works.

Finally, f(g(x)) a composite function.

Which means that f is a function of g which is a function of x.

The amount of money Raul earns f, depends of number of tickets he sells g, and that depends on the number of hours he works x.

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

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

See explanation

Step-by-step explanation:

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.

So, the function f(g(x)) represents the amount of money Raul earns, where x is the number of hours he works.

If

then