At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Given the functions:
[tex]\[ f(x) = -2x - 3 \][/tex]
[tex]\[ g(x) = 3x + 1 \][/tex]

Find [tex]\((f \cdot g)(x)\)[/tex].

A. [tex]\(-6x^2 - 3\)[/tex]
B. [tex]\(-6x^2 - 11x - 3\)[/tex]
C. [tex]\(-6x^3 - 11x^2 - 3x\)[/tex]
D. [tex]\(-6x^2 - 7x - 3\)[/tex]

Sagot :

To find [tex]\((f \cdot g)(x)\)[/tex] where [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] are given by:

[tex]\[ f(x) = -2x - 3 \][/tex]
[tex]\[ g(x) = 3x + 1 \][/tex]

We need to multiply these two functions together. This process involves using the distributive property (also known as the FOIL method for binomials):

[tex]\[ (f \cdot g)(x) = f(x) \cdot g(x) \][/tex]

Substitute the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:

[tex]\[ (f \cdot g)(x) = (-2x - 3) \cdot (3x + 1) \][/tex]

Next, we distribute each term in the first binomial by each term in the second binomial:

[tex]\[ = (-2x \cdot 3x) + (-2x \cdot 1) + (-3 \cdot 3x) + (-3 \cdot 1) \][/tex]

Now, calculate each term:

[tex]\[ = (-2x \cdot 3x) + (-2x \cdot 1) + (-3 \cdot 3x) + (-3 \cdot 1) = -6x^2 - 2x - 9x - 3 \][/tex]

Combine the like terms:

[tex]\[ -6x^2 - 2x - 9x - 3 = -6x^2 - 11x - 3 \][/tex]

So the final result for [tex]\((f \cdot g)(x)\)[/tex] is:

[tex]\[ (f \cdot g)(x) = -6x^2 - 11x - 3 \][/tex]

Answer:

hello

Step-by-step explanation:

f(x) = -2x-3

g(x)=3x+1

(f.g)x

(-2x-3)(3x+1)

=-2x*3x -2x*1 -3*3x -3*1

=-6x²-2x-9x-3

=6x²-11x-3 (B)