Question

Given the functions f(x) = −3x + 1 and g(x) = −2x − 3, which operation, f + g, f − g, or f ⋅ g, results in the smallest coefficient on the x term?

Answer 1

Performing the operations on the functions f(x) = -3x + 1 and g(x) = -2x - 3, we find that f - g gives us the smallest coefficient for the x term, which is -1.

Step-by-step explanation:

The question involves finding which operation, f + g, f − g, or f ⋅ g, results in the smallest coefficient on the x term given the functions f(x) = −3x + 1 and g(x) = −2x − 3.

Let's perform each operation one by one and find the resulting coefficients on the x term:

• f + g: (-3x + 1) + (-2x - 3) = -3x - 2x + 1 - 3 = -5x - 2.
• f − g: (-3x + 1) - (-2x - 3) = -3x + 2x + 1 + 3 = -x + 4.
• f ⋅ g: (-3x + 1) ⋅ (-2x - 3) = 6x2 + 9x - 2x - 3 = 6x2 + 7x - 3.

From the calculations above, we can see that the operation f − g produces the smallest coefficient on the x term, which is -1.