Answer:To find (f × g)(x), we need to find the product of the two functions f(x) and g(x), which is written as:
(f × g)(x) = f(x) × g(x)
First, let's find g(x):
g(x) = 2x³ - 4
Next, we'll substitute this into the expression for (f × g)(x):
(f × g)(x) = f(x) × g(x)
= (x² - 2x + 4) × (2x³ - 4)
We can simplify this by distributing the terms:
= 2x³ (x² - 2x + 4) - 4 (x² - 2x + 4)
= 2x⁵ - 4x³ + 8x³ - 4x² + 8x - 16
Simplifying further:
(f × g)(x) = 2x⁵ - 4x³ - 4x² + 8x - 16
Therefore, (f × g)(x) = 2x⁵ - 4x³ - 4x² + 8x - 16.
Explanation: