Question

find and simplify the function $(f \cdot g)(x)$ where, $f(x) = 3x - 2$ and $g(x) = x - 3$. select one: a. $(f \cdot g)(x) = -3x^2 - 11x + 6$ b. $(f \cdot g)(x) = 3x^2 - 7x - 6$ c. $(f \cdot g)(x) = 3x^2 - 11x - 6$ d. $(f \cdot g)(x) = 3x^2 - 11x + 6$

Explanation:

Step1: Define product of functions

$(f \cdot g)(x) = f(x) \cdot g(x)$

Step2: Substitute given functions

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

Step3: Expand using distributive property

$(3x)(x) + (3x)(-3) + (-2)(x) + (-2)(-3)$
$= 3x^2 - 9x - 2x + 6$

Step4: Combine like terms

$3x^2 + (-9x - 2x) + 6 = 3x^2 - 11x + 6$

Answer:

D. $(f \cdot g)(x) = 3x^2 - 11x + 6$