Answer
(a.)$(fg)(x)=x^3+27$.
(b.)19.
(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.
$(fg)(-2)=19$.
(c.) Plug $x=0$ into function (1).
$(fg)(0)=(0)^3+27$
Clear the parentheses.
$(fg)(0)=0+27$
Simplify.
$(fg)(0)=27$.
