Question

Let f(x) = 4x + 8 and g(x) = 2x - 12. Perform the function operation, (f - g)
(x), and then find the domain of the result.

Answer 1

Answer:

See below.

Step-by-step explanation:

So we know that:

$f(x)=4x+8\text{ and } g(x)=2x-12$

First, know that:

$(f-g)(x)$

Is the same as:

$=f(x)-g(x)$

Substitute:

$=(4x+8)-(2x-12)$

Distribute:

$=4x+8-2x+12$

Combine like terms;

$=2x+20$

Thus:

$f(g(x))=2x+20$

This is simply a linear equation.

Thus, the domain is all real numbers.

In interval notation, this is:

$(-\infty, \infty)$