Question

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

Answer 1

all work is shown and pictured

Answer 2

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`