We want to perform $f(x)$ and $g(x).$

### Calculating $f(x)+g(x)$

Let's substitute the given function rules into the expressions

$f(x)$ and

$g(x).$ Then we will perform the addition.

$f(x)+g(x)$

$3x+(-2x+6)$

$3x−2x+6$

$x+6$

After we have performed the addition, the result takes the form of

$x+6.$
$f(x)+g(x)=x+6 $ ### Calculating $f(x)−g(x)$

Let's substitute the given function rules into the expressions

$f(x)$ and

$g(x).$ Then we will perform the subtraction.

$f(x)−g(x)$

$3x−(-2x+6)$

$3x+2x−6$

$5x−6$

After we have performed the subtraction, the result takes the form of

$5x−6.$
$f(x)−g(x)=5x−6 $ ### Calculating $f(x)⋅g(x)$

Let's substitute the given function rules into the expressions

$f(x)$ and

$g(x).$ Then we will perform the multiplication.

$f(x)⋅g(x)$

$3x⋅(-2x+6)$

$-6x_{2}+18x$

After we have performed the multiplication, the result takes the form of

$-6x_{2}+18x.$
$f(x)⋅g)(x)=-6x_{2}+18x $ ### Calculating $g(x)f(x) $

To perform the division, let's substitute the given function rules into the expressions

$f(x)$ and

$g(x).$
This expression cannot be simplified any further. The of both

$f(x)$ and

$g(x)$ is all ,

$R.$ The domain of

$g(x)f(x) $ is the set of numbers common to the domains of both

$f(x)$ and

$g(x).$ However, the denominator

**cannot** be

$0.$ Let's find the values that make

$g(x)=0.$
$g(x)=0$

$-2x+6=0$

$-2x=-6$

$x=-2-6 $

$x=3$

As we can see,

$x=3$ makes

$g(x)=0.$ Therefore, this value must be excluded from the domain of the quotient. We can say that the domain is the set of all real numbers except

$3.$
$g(x)f(x) =-2x+63x ,x =3 $