Let `[x]` be defined by the equation `[x] = (x^2)/2`. Then which one of the following equals 2?

Options

A. [2]
B. [4]
C. [6]
D. [8]

Answer

To solve the problem, we need to evaluate the function defined as \([x] = \frac{x^2}{2}\) for the values 2, 4, 6, and 8, and determine which one yields a result of 2.

### Step-by-Step Solution:

1. **Evaluate for \(x = 2\)**:
\[ [2] = \frac{2^2}{2} = \frac{4}{2} = 2 \]
So, \([2] = 2\).

2. **Evaluate for \(x = 4\)**:
\[ [4] = \frac{4^2}{2} = \frac{16}{2} = 8 \]
So, \([4] = 8\).

3. **Evaluate for \(x = 6\)**:
\[ [6] = \frac{6^2}{2} = \frac{36}{2} = 18 \]
So, \([6] = 18\).

4. **Evaluate for \(x = 8\)**:
\[ [8] = \frac{8^2}{2} = \frac{64}{2} = 32 \]
So, \([8] = 32\).

### Conclusion:
From the evaluations:
- \([2] = 2\)
- \([4] = 8\)
- \([6] = 18\)
- \([8] = 32\)

The only value that equals 2 is \([2]\).

### Final Answer:
The correct option is \([2] = 2\).

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