Question

Let f(x) = -2x + 7 and g(x) = -6x + 3. Find fxg and state its domain.

Answer 1

Option D: $(f\times g)(x)=12 x^{2}-48 x+21$; all real numbers.

Explanation:

Given that the functions are $f(x)=-2 x+7$ and $g(x)=-6 x+3$

We need to determine the value of $(f\times g)(x)$ and its domain.

The value of $(f\times g)(x)$:

The value of $(f\times g)(x)$ can be determined by multiplying the two functions.

Thus, we have,

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

                $=(-2x+7)(-6x+3)$

                $=12x^2-6x-42x+21$

$(f\times g)(x)=12 x^{2}-48 x+21$

Thus, the value of $(f\times g)(x)$ is $(f\times g)(x)=12 x^{2}-48 x+21$

Domain:

We need to determine the domain of the function $(f\times g)(x)$

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 $(f\times g)(x)=12 x^{2}-48 x+21$ has no undefined constraints, the function is well defined for all real numbers.

Hence, Option D is the correct answer.

Answer 2

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