Question

Raul works at a movie theatre. The function f(x) represents the amount of money in dollars 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) = 3x2 + 16

g(x) = the square root of five times x cubed

Find f(g(x)).

Answer 1

Answer:

$f(g(x))=15x^3+16$.

Step-by-step explanation:

The given functions are

$f(x)=3x^2+16$

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

We need to find the function f(g(x)).

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

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

On simplification, we get

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

$f(g(x))=15x^3+16$

Therefore, the required function is $f(g(x))=15x^3+16$.

Answer 2

Answer:

Step-by-step explanation:

The function f(x) represents the amount of money in dollars Raul earns per ticket, where x is the number of tickets he sells. This is represented by the function,

f(x) = 3x2 + 16 - - - - - - -1

The function g(x) represents the number of tickets Raul sells per hour, where x is the number of hours he works. The function is represented by

g(x) = the square root of five times x cubed

g(x) = √(5x^3)

To find f(g(x)), we substitute g(x) into f(x).

f(g(x))= 3[√(5x^3)]^2 + 16