Answer
(a.)$(fg)(x)=x^3-27$.
(b.)-35.
(c.)-27.
Work Step by Step
The given functions are
$f(x)=x-3$ and $g(x)=x^2+3x+9$
(a.) $(fg)(x)=f(x)\times g(x)$
Plug both functions.
$(fg)(x)=(x-3)\times (x^2+3x+9)$
Multiply the second bracket by each term of the first bracket.
$(fg)(x)=x\times (x^2+3x+9)-3\times (x^2+3x+9)$
Clear the parentheses.
$(fg)(x)=x^3+3x^2+9x-3x^2-9x-27$
Simplify.
$(fg)(x)=x^3-27$ ...... (1)
(b.) Plug $x=-2$ into function (1).
$(fg)(-2)=(-2)^3-27$
Clear the parentheses.
$(fg)(-2)=-8-27$
Simplify.
$(fg)(-2)=-35$.
(c.) Plug $x=0$ into the function (1).
$(fg)(0)=(0)^3-27$
Clear the parentheses.
$(fg)(0)=0-27$
Simplify.
$(fg)(0)=-27$.
