Question

If g(n)=2n+3 and h(n)=−2n2−2n, find (g⋅h)(n).

a) 2n2+4n−3
b) −4n²−4n+3
c) −2n²−2n+3
d) 4n2+4n−3

Answer 1

To find the product (g⋅h)(n), we multiply the functions g(n) = 2n + 3 and h(n) = −2n² − 2n together. After multiplying and combining like terms, the result is −4n³ − 10n² − 6n. However, this does not match any of the provided answer choices.

Step-by-step explanation:

To find the product (g⋅h)(n) of the two functions g(n) and h(n), where g(n) = 2n + 3 and h(n) = −2n² − 2n, we need to multiply the two functions together.

1. Multiply the constant from g(n) by each term in h(n): (3)(−2n²) + (3)(−2n) = −6n² − 6n.
2. Multiply the linear term from g(n) by each term in h(n): (2n)(−2n²) + (2n)(−2n) = −4n³ − 4n².
3. Combine like terms from the products of the multiplications in the previous steps: −4n³ − 4n² − 6n² − 6n.
4. After combining like terms, our expression simplifies to −4n³ − 10n² − 6n.

However, none of the provided answer choices exactly match our result, which suggests there may be an error in the provided answers or a misunderstanding of the question.