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

See below.

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)`