Answer
(a.) $(fg)(x)=x^2+4x-12$.
(b.) $(fg)(-1)=-15$.
(c.) $(fg)(0)=-12$.
Work Step by Step
The given functions are
$f(x)=x-2$ and $g(x)=x+6$
(a.) $(fg)(x)=f(x)\times g(x)$
Plug both functions.
$(fg)(x)=(x-2)\times (x+6)$
Multiply the second bracket by each terms of the first bracket.
$(fg)(x)=x\times (x+6)-2\times (x+6)$
Clear the parentheses.
$(fg)(x)=x^2+6x-2x-12$
Simplify.
$(fg)(x)=x^2+4x-12$ ...... (1)
(b.) Plug $x=-1$ into function (1).
$(fg)(-1)=(-1)^2+4(-1)-12$
Clear the parentheses.
$(fg)(-1)=1-4-12$
Simplify.
$(fg)(-1)=-15$.
(c.) Plug $x=0$ into the function (1).
$(fg)(0)=(0)^2+4(0)-12$
Clear the parentheses.
$(fg)(0)=0+0-12$
Simplify.
$(fg)(0)=-12$.
