Question

select the correct answer. function ( h ) is the product of functions ( f ) and ( g ). ( f(x) = 2x + 5 ) ( g(x) = 6x - 9 ) which equation defines function ( h )? a. ( h(x) = 12x^2 - 4x - 45 ) b. ( h(x) = 12x - 45 ) c. ( h(x) = 12x^2 - 45 ) d. ( h(x) = 12x^2 + 12x - 45 )

Explanation:

Step1: Recall the product of two functions

To find the product of two functions \( f(x) \) and \( g(x) \), we use the formula \( h(x)=f(x)\times g(x) \). Given \( f(x) = 2x + 5 \) and \( g(x)=6x - 9 \), we need to multiply these two binomials.

Step2: Apply the distributive property (FOIL method)

\[

$$\begin{align*} h(x)&=(2x + 5)(6x - 9)\\ &=2x\times6x+2x\times(-9)+5\times6x + 5\times(-9)\\ &=12x^{2}-18x + 30x-45\\ &=12x^{2}+12x - 45 \end{align*}$$

\]

Answer:

D. \( h(x)=12x^{2}+12x - 45 \)