Answer :
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]
[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)