Question

If$\,\,x \oplus y = \frac{x}{2} - y\,\,$and$\,x * y = \frac{y}{3} - 2x\,\,$then find the value of $(3 \oplus 1) * (4 \oplus -4)$.

• A. -1
• B. 0
• C. 1
• D. 2

Answer 1

Answer:

C. 1

The Combined Formula Method

We are given the two operations:

1. $x \oplus y = \frac{x}{2} - y$

2. $A * B = \frac{B}{3} - 2A$

We want to find the value of $(3 \oplus 1) * (4 \oplus -4)$.

Let's substitute the inner operations directly into the outer $*$ formula:

$\text{Value} = \frac{(4 \oplus -4)}{3} - 2(3 \oplus 1)$

Now, substitute the definition of $\oplus$ for both parts inside the structure:

$\text{Value} = \frac{\left(\frac{4}{2} - (-4)\right)}{3} - 2\left(\frac{3}{2} - 1\right)$

Now, simplify from left to right:

1. Simplify the fractions inside the brackets:
   $\text{Value} = \frac{(2 + 4)}{3} - 2\left(1.5 - 1\right)$

2. Solve the terms:
   $\text{Value} = \frac{6}{3} - 2(0.5)$

3. Final Calculation:
   $\text{Value} = 2 - 1 = \mathbf{1}$