Question

If f(x)=2x−3 and g(x)=4x+5, what is (f⋅g)(x)?A. (f⋅g)(x)=8x2+22x−15B. (f⋅g)(x)=8x−15C. (f⋅g)(x)=6x+2D. (f⋅g)(x)=8x2−2x−15

Answer 1

Given the functions:

$\begin{gathered} f(x)=2x-3 \\ \\ g(x)=4x+5 \end{gathered}$

You need to multiply them in order to find:

$(f\cdot g)(x)$

Then, you need to set up:

$(f\cdot g)(x)=(2x-3)(4x+5)$

In order to multiply the binomials, you can use the FOIL Method, which states that:

$(a+b)(c+d)=ac+ad+bc+bd$

You also need to remember the Sign Rules for Multiplication:

$\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}$

Then, you get:

$(f\cdot g)(x)=(2x)(4x)+(2x)(5)-(3)(4x)-(3)(5)$$(f\cdot g)(x)=8x^2+10x-12x-15$

Now you have to add the like terms (these are the terms that have the same variables with the same exponents):

$(f\cdot g)(x)=8x^2-2x-15$

Hence, the answer is: Option D.