Question

Given the functions f(x) = 3x - 1 and g(x) = 3x + 4, which operation results in the smallest coefficient on the x term?

A) Addition
B) Subtraction
C) Multiplication
D) Two operations result in the same coefficient

Answer 1

The operation of subtraction, when applied to f(x) = 3x - 1 and g(x) = 3x + 4, results in the smallest coefficient on the x term, which is zero in the resultant expression 0x - 5.

Step-by-step explanation:

The question is asking which operation (addition, subtraction, multiplication) results in the smallest coefficient on the x term when applied to the functions f(x) = 3x - 1 and g(x) = 3x + 4. To find the solution, we perform each operation:

• Addition (A): f(x) + g(x) = (3x - 1) + (3x + 4) = 6x + 3.
• Subtraction (B): f(x) - g(x) = (3x - 1) - (3x + 4) = 0x - 5.
• Multiplication (C): f(x) * g(x) = (3x - 1)(3x + 4) which expands to 9x^2 + 9x - 4. The coefficient of the x term is 9, which is greater than in addition or subtraction.

Subtraction results in no x term at all, so the coefficient is effectively zero, making subtraction the operation that results in the smallest coefficient on the x term.