Question

F ( x ) = x 2 − 4 x 3 f(x)=x2-4x 3 g ( x ) = x − 1 g(x)=x-1. Find (f⋅g)(x), the product of f(x) and g(x)?

a) x³−5x²+4x³
b) x³−5x²+4x
c) x³−5x²−4x
d) x³−5x²−4x³

Answer 1

The product of the functions f(x) = x^2 - 4x^3 and g(x) = x - 1 results in -4x^4 + 5x^3 - x^2, which is not listed among the options provided. This suggests there is an error in the options.

Step-by-step explanation:

To find the product of two functions (f\(x\) = x^2 - 4x^3 and g\(x\) = x - 1), you must multiply each term in the first function by each term in the second function.

Beginning with the multiplication process:

• x^2 multiplied by x is x^3.
• x^2 multiplied by (-1) is -x^2.
• -4x^3 multiplied by x is -4x^4.
• -4x^3 multiplied by (-1) is +4x^3.

After multiplying we combine the terms:

• x^3 - x^2 + 4x^3 - 4x^4.

Combining like terms gives:

• -4x^4 + (1+4)x^3 - x^2
• -4x^4 + 5x^3 - x^2

Thus, the product of f\(x\) and g\(x\), which is denoted as (f\cdot g)(x), is -4x^4 + 5x^3 - x^2, which is not one of the options provided. Therefore, there must be a mistake in the given options.