Final answer:
The difference quotient is not clearly defined in the question, so the function is simplified and then evaluated at the specified values, resulting in f(3/2) = 2, f(3x) = 6x - 1, f(2x+1) = 4x + 1, and f(3) = 5.
Step-by-step explanation:
The question asks for the evaluation of a difference quotient for a function, which appears to be incorrectly represented as f(x) = 3x - x - 1. A difference quotient typically involves a function f(x), and it is in the form of (f(x+h)-f(x))/h. However, since the question doesn't give us a function with 'h' nor does it ask for a particular value of 'h', there might be some confusion. In the absence of a clear difference quotient setup, let's correct the function first. The provided function simplifies to f(x) = 2x - 1.
Now, if we were to evaluate this function at different values of x as implied by the given choices, a student might simply replace 'x' with the values provided in options a through d and find out the value of the function at those values. Assuming that's what the question seeks, here are the evaluated forms:
- For 3/2, f(3/2) = 2(3/2) - 1 = 3 - 1 = 2.
- For 3x, f(3x) = 2(3x) - 1 = 6x - 1.
- For 2x+1, f(2x+1) = 2(2x+1) - 1 = 4x + 1.
- For 3, f(3) = 2(3) - 1 = 6 - 1 = 5.