Question

name: mp2 test 2 review

1. the functions f and g are defined as $f(x) = 2x^2$ and $g(x) = 4x$. write a function equal to $h(x) = \frac{f(3x)g(-x)}{2}$ and simplify.

Explanation:

Step1: Find \( f(3x) \)

Given \( f(x) = 2x^2 \), substitute \( x = 3x \) into \( f(x) \).
\( f(3x)=2(3x)^2 = 2\times9x^2 = 18x^2 \)

Step2: Find \( g(-x) \)

Given \( g(x) = 4x \), substitute \( x=-x \) into \( g(x) \).
\( g(-x)=4(-x)= -4x \)

Step3: Substitute \( f(3x) \) and \( g(-x) \) into \( h(x) \)

\( h(x)=\frac{f(3x)g(-x)}{2}=\frac{18x^2\times(-4x)}{2} \)
First, multiply the numerator: \( 18x^2\times(-4x)= -72x^3 \)
Then divide by 2: \( \frac{-72x^3}{2}=-36x^3 \)

Answer:

\( h(x)= -36x^3 \)