Question

name: jeshua amara mp2 test 2 review

1. the functions f and g are defined as f(x) = 2x² and g(x) = 4x. write a function equal to h(x) = (f(3x)g(-x))/2 and simplify.

Explanation:

Step1: Compute $f(3x)$

Substitute $3x$ into $f(x)=2x^2$:
$f(3x)=2(3x)^2=2\times9x^2=18x^2$

Step2: Compute $g(-x)$

Substitute $-x$ into $g(x)=4x$:
$g(-x)=4(-x)=-4x$

Step3: Multiply $f(3x)$ and $g(-x)$

Calculate the product of the two results:
$f(3x)g(-x)=18x^2\times(-4x)=-72x^3$

Step4: Divide by 2 and simplify

Divide the product by 2 to get $h(x)$:
$h(x)=\frac{-72x^3}{2}=-36x^3$

Answer:

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