Option D: [tex](f\times g)(x)=12 x^{2}-48 x+21[/tex]; all real numbers.
Explanation:
Given that the functions are [tex]f(x)=-2 x+7[/tex] and [tex]g(x)=-6 x+3[/tex]
We need to determine the value of [tex](f\times g)(x)[/tex] and its domain.
The value of [tex](f\times g)(x)[/tex]:
The value of [tex](f\times g)(x)[/tex] can be determined by multiplying the two functions.
Thus, we have,
[tex](f\times g)(x)=f(x)\times g(x)[/tex]
[tex]=(-2x+7)(-6x+3)[/tex]
[tex]=12x^2-6x-42x+21[/tex]
[tex](f\times g)(x)=12 x^{2}-48 x+21[/tex]
Thus, the value of [tex](f\times g)(x)[/tex] is [tex](f\times g)(x)=12 x^{2}-48 x+21[/tex]
Domain:
We need to determine the domain of the function [tex](f\times g)(x)[/tex]
The domain of the function is the set of all independent x - values for which the function is real and well defined.
Thus, the function [tex](f\times g)(x)=12 x^{2}-48 x+21[/tex] has no undefined constraints, the function is well defined for all real numbers.
Hence, Option D is the correct answer.
Answer:
12x² - 48x + 21; all real numbers
Step-by-step explanation:
f(x) = -2x + 7
g(x) = -6x + 3
f(x)×g(x) = (-2x + 7)(-6x + 3)
= 12x² - 42x - 6x + 21
= 12x² - 48x + 21
