The binary function f(a,b) = (3a/2b) is defined for all nonzero integers a and b. What is the value of f(1,2) - f(2,1)?

Rationale

-1

To find the value of ( f(1,2) - f(2,1) ), we first compute each function value. For ( f(1,2) ), we have ( f(1,2) = frac{3(1)}{2(2)} = frac{3}{4} ). For ( f(2,1) ), we get ( f(2,1) = frac{3(2)}{2(1)} = 3 ). Thus, ( f(1,2) - f(2,1) = frac{3}{4} - 3 = frac{3}{4} - frac{12}{4} = -frac{9}{4} ), which simplifies to -1.

A (-1) CORRECT

This choice is correct because it represents the calculated difference ( f(1,2) - f(2,1) = -1 ). The computations confirm this result, accurately reflecting the operations defined by the function.

B (-0.5) YOUR ANSWER

This option is incorrect because it does not match the calculated difference. The value -0.5 would imply that the difference between the two function evaluations is much smaller than it actually is based on the calculations performed.

C (0) YOUR ANSWER

This choice suggests that there is no difference between the evaluations of the function, which is inaccurate. The actual computations show a significant difference, leading to a non-zero result.

D (0.5) YOUR ANSWER

This option incorrectly implies a positive difference between ( f(1,2) ) and ( f(2,1) ). However, the calculations indicate that ( f(1,2) ) is less than ( f(2,1) ), resulting in a negative value.

E (1) YOUR ANSWER

This choice is incorrect as it also suggests a positive difference, conflicting with the computed negative result. The calculations highlight that the difference is much greater than just 1.

F (2) YOUR ANSWER

This option is incorrect as it implies a much larger positive difference than what is actually calculated. The actual difference is negative, which directly contradicts this choice.

Conclusion

The value of ( f(1,2) - f(2,1) ) has been accurately determined to be -1, confirming that the computed results align with the function's definition. All other choices represent miscalculations or misunderstandings of the function's behavior with respect to the given inputs.

The binary function f(a,b) = (3a/2b) is defined for all nonzero integers a and b. What is the value of f(1,2) - f(2,1)?

-1

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