Question

Two functions are shown.
f(x) = x^2 + 2x - 5
g(x) = 2x + 4
What is (f·g)(x)?

Answer 1

To calculate (f·g)(x), multiply each term of f(x) = x^2 + 2x - 5 by each term of g(x) = 2x + 4 and sum the products. The resultant function is (f·g)(x) = 2x^3 + 8x^2 - 2x - 20.

Step-by-step explanation:

To find the product (f·g)(x) of two functions f(x) and g(x), we must multiply them together. Given functions f(x) = x^2 + 2x - 5 and g(x) = 2x + 4, we can find the product by distributing each term of g(x) across f(x).

Let's compute this step by step:

1. Multiply x^2 of f(x) by 2x and 4 of g(x) separately. This gives 2x^3 and 4x^2.
2. Multiply 2x of f(x) by 2x and 4 of g(x) separately. This gives 4x^2 and 8x.
3. Multiply -5 of f(x) by 2x and 4 of g(x) separately. This gives -10x and -20.
4. Add all the products together to get (f·g)(x) = 2x^3 + 8x^2 - 2x - 20.

Therefore, the product of the functions is (f·g)(x) = 2x^3 + 8x^2 - 2x - 20.