Answer:
[tex](r\cdot s)(x)=3x^3-3x^2[/tex]
[tex](r+s)(x)=3x^2+x-1[/tex]
[tex](r-s)(-3)=-31[/tex]
Step-by-step explanation:
[tex](r \cdot s)(x)[/tex] means we are multiplying the functions mentioned.
[tex](x-1)(3x^2)[/tex]
Distribute:
[tex]3x^3-3x^2[/tex]
-------
[tex](r+s)(x)[/tex]
This means we are adding the mentioned functions.
[tex](x-1)+(3x^2)[/tex]
No like terms to combine so we are going to rearrange in standard form:
[tex]3x^2+x-1[/tex]
----
[tex](r-s)(-3)[/tex]
Replace the x's in both functions with -3, then we will simplify the difference of [tex]r(-3)[/tex] and [tex]s(-3)[/tex].
[tex]r(x)=x-1[/tex]
[tex]r(-3)=-3-1=-4[/tex]
[tex]s(x)=3x^2[/tex]
[tex]s(-3)=3(-3)^2=3(9)=27[/tex]
So now we do -4-27=-31.
