For this case we have the following functions:
[tex]f (x) = 9x ^ 2-2x-9\\g (x) = 11x-9[/tex]
We must find [tex](f * g) (x)[/tex]. By definition we have to:
[tex](f * g) (x) = f (x) * g (x)[/tex]
So:
[tex](f * g) (x) = (9x ^ 2-2x-9) (11x-9)[/tex]
We apply distributive property considering that:
[tex]+ * - = -\\- * - = +[/tex]
To multiply powers of the same base, we place the same base and add the exponents:
[tex](f * g) (x) = 99x ^ 3-81x ^ 2-22x ^ 2 + 18x-99x + 81\\(f * g) (x) = 99x ^ 3-103x ^ 2-81x + 81[/tex]
Answer:
[tex](f * g) (x) = 99x ^ 3-103x ^ 2-81x + 81[/tex]
