Question

For the given functions f and g, find the requested function and state its domain. f(x) = 8 - 2x; g(x) = -4x², find f * g.

Answer 1

To find f * g, multiply the functions f(x) and g(x). The function f * g is -32x² + 8x³ with a domain of all real numbers.

Step-by-step explanation:

To find the function f * g, we need to multiply the two given functions f(x) and g(x).

f(x) = 8 - 2x and g(x) = -4x²

To multiply the functions, we substitute g(x) into f(x) to get:

f * g = (8 - 2x) * (-4x²)

Expanding and simplifying, we have:

f * g = -32x² + 8x³

The domain of f * g is the set of all real numbers, as there are no restrictions on input values for the given functions.