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

Answer 1

@Shadow

Answer 2

do you know were to start?

Answer 3

honestly no

Answer 4

how confortable with algebra are you?

Answer 5

I just want to make sure you are aware how to solve functions and such

Answer 6

i understand most things but square roots mess me up

Answer 7

okay cool

Answer 8

essentially f(g(x)) means you need to input g(x) into the x terms of th f(x) equation

Answer 9

ok so f(g(x)) = 2(sqrt 5x^3)^2+16 ?

Answer 10

that is correct

Answer 11

ok so what do i do to solve

Answer 12

more like where do i start?

Answer 13

you need to distribute the parentesis

Answer 14

so the new equation would be 2(squrt5^3)(squrt5^3)+ 16

Answer 15

you know what im gonna invite someone over to help. Im in the middle of history so my mind isnt right for math.

Answer 16

@mhchen

Answer 17

sorry I was working on another question while i waited and got carried away

Answer 18

is
\[g(x) = \sqrt{5x^{3}}\]
?

Answer 19

Yes

Answer 20

so
\[f(g(x)) = 2(\sqrt{5x^{3}})^{2}+16\]
right?

Answer 21

yes that is what I got so far

Answer 22

Then
\[f(g(x)) = 2(5x^{3})+16\]
right?

Answer 23

ok i get that

Answer 24

Then
\[f(g(x)) = 10x^{3}+16\]
right?

Answer 25

yes ok

Answer 26

Yeah...that's the most you can do.

So

"f(x) represents the amount of money Raul earns per ticket, where x is the number of tickets he sells"
and that means
Raul's money = x ticket sold.

"g(x) represents the number of tickets Raul sells per hour, where x is the number of hours he works"
and that means
tickets sold = x hours.

right?

Answer 27

thank you so much you really did help me.