Question

Find (f*g) (x) for the following functions. f(x) = 9x2 – 2x – 9 g(x) = 11x – 9

Answer 1

For this case we have the following functions:

$f (x) = 9x ^ 2-2x-9\\g (x) = 11x-9$

We must find $(f * g) (x)$. By definition we have to:

$(f * g) (x) = f (x) * g (x)$

So:

$(f * g) (x) = (9x ^ 2-2x-9) (11x-9)$

We apply distributive property considering that:

$+ * - = -\\- * - = +$

To multiply powers of the same base, we place the same base and add the exponents:

$(f * g) (x) = 99x ^ 3-81x ^ 2-22x ^ 2 + 18x-99x + 81\\(f * g) (x) = 99x ^ 3-103x ^ 2-81x + 81$

Answer:

$(f * g) (x) = 99x ^ 3-103x ^ 2-81x + 81$

Answer 2

Answer:

all work is shown and pictured