Final answer:
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.