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))f(x) = 2x2 + 16g(x) = /5x^3

Answer 1

Given the functions

`\begin{gathered} f(x)=2x^2+16 \\ g(x)=\sqrt[]{5x^3} \end{gathered}`

First, we get the composite function

`f(g(x))=f(\sqrt[]{5x^3})`

To get f(√5x³), we will substitute x in f(x) with √5x³ as shown:

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

The square root and power 2 cancel each other

`\begin{gathered} f(g(x))=2(5x^3)+16 \\ \text{Simplify} \\ f(g(x))=10x^3+16 \end{gathered}`

Answer:

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