Question

study these equations:
f(x) = 2x - 4
g(x) = 3x + 1
what is h(x) = f(x)g(x)?
h(x) = 6x² - 10x - 4
h(x) = 6x² - 12x - 4
h(x) = 6x² + 2x - 4
h(x) = 6x² + 14x + 4

Explanation:

Step1: Substitute the functions

We know that \( f(x) = 2x - 4 \) and \( g(x) = 3x + 1 \), so \( h(x)=f(x)g(x)=(2x - 4)(3x + 1) \).

Step2: Use the distributive property (FOIL method)

First, multiply the First terms: \( 2x\times3x = 6x^{2} \).
Then, multiply the Outer terms: \( 2x\times1 = 2x \).
Next, multiply the Inner terms: \( - 4\times3x=-12x \).
Finally, multiply the Last terms: \( - 4\times1=-4 \).

Step3: Combine like terms

Now, combine the middle terms: \( 2x-12x=-10x \).
So, \( h(x)=6x^{2}-10x - 4 \).

Answer:

\( h(x)=6x^{2}-10x - 4 \) (the first option)