Question

If f(x)=4x−5 and g(x)=6−3x, what is f(x)g(x)?

a) (4x - 5)(6 - 3x)
b) (4x - 5) + (6 - 3x)
c) (4x - 5)/(6 - 3x)
d) (4x - 5)² + (6 - 3x)²

Answer 1

To find f(x)g(x) for f(x) = 4x - 5 and g(x) = 6 - 3x, we multiply the two functions, resulting in -12x^2 + 39x - 30, which matches option a) (4x - 5)(6 - 3x).

Step-by-step explanation:

If f(x) = 4x - 5 and g(x) = 6 - 3x, to find f(x)g(x), we multiply the two functions together. Multiplying two polynomials involves using the distributive property (also known as the FOIL method for binomials). We multiply each term in the first polynomial by each term in the second polynomial and then combine like terms.

So, f(x)g(x) is calculated as follows:

1. Multiply 4x by 6 to get 24x.
2. Multiply 4x by -3x to get -12x^2.
3. Multiply -5 by 6 to get -30.
4. Multiply -5 by -3x to get +15x.

Combining like terms, we get -12x^2 + 24x + 15x - 30, which simplifies to -12x^2 + 39x - 30.

Therefore, the product f(x)g(x) corresponds to option a) (4x - 5)(6 - 3x).