For this case we have by definition that:
[tex](f * g) (x) = f (x) * g (x)[/tex]
In this case we must find [tex](w* r) (x)[/tex], so:
[tex](w * r) (x) = w (x) * r (x) = (x-2) (2-x ^ 2) =[/tex]
We must apply distributive property that states that:
[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]
So:
[tex](x-2) (2-x ^ 2) = 2x-x ^ 3-4 + 2x ^ 2 = -x ^ 3 + 2x ^ 2 + 2x-4[/tex]
The range is the set of all "y" values
Valid That is to say: (-∞,∞)
Answer:
(-∞,∞)
