Question

Suppose f(x)=10x−8 and g(x)=10x²−x. Find (fg)(x).

Answer 1

f of g of x is a composite function that is represented by f(g(x)) (or) (f ∘ g)(x). To find f(g(x)), substitute g(x) into f(x). To find the domain of f(g(x)), find the domain of both the inner function g(x) and the resultant function f(g(x)) and then compute the intersection.

Answer 2

To find the product of the functions f(x) and g(x), denoted as (fg)(x), multiply each term of f(x) by each term of g(x), combine like terms, and simplify the resulting expression.

Step-by-step explanation:

When looking to find the product of two functions, (fg)(x), where f(x) = 10x - 8 and g(x) = 10x² - x, we multiply the two functions together. This process is straight-forward – simply multiply each term in the first function by each term in the second function.

The multiplication process goes as follows:

1. Multiply 10x (from f(x)) by 10x² (from g(x)) to get 100x³.
2. Multiply 10x (from f(x)) by -x (from g(x)) to get -10x².
3. Multiply -8 (from f(x)) by 10x² (from g(x)) to get -80x².
4. Multiply -8 (from f(x)) by -x (from g(x)) to get 8x.

Sum up the results to get the final expression for (fg)(x). Making sure we combine like terms, we get:

(fg)(x) = 100x³ - 10x² - 80x² + 8x

After combining the -10x² and -80x² terms, we get the final simplified answer:

(fg)(x) = 100x³ - 90x² + 8x