Question

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

-14x^2 + 36x - 18; all real numbers except x = 7


-14x^2 + 36x - 18; all real numbers


12x^2 - 48x + 21; all real numbers except x = 1


12x^2 - 48x + 21; all real numbers

Answer 1

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

Answer 2

Option D:
`(f* g)(x)=12 x^(2)-48 x+21`; all real numbers.

Step-by-step 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* g)(x)` and its domain.

The value of
`(f* g)(x)`:

The value of
`(f* g)(x)` can be determined by multiplying the two functions.

Thus, we have,

`(f* g)(x)=f(x)* g(x)`

`=(-2x+7)(-6x+3)`

`=12x^2-6x-42x+21`

`(f* g)(x)=12 x^(2)-48 x+21`

Thus, the value of
`(f* g)(x)` is
`(f* g)(x)=12 x^(2)-48 x+21`

Domain:

We need to determine the domain of the function
`(f* 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* 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.