If `f(x)=|x|+[x]`, where [x] is the greatest integer less than or equal to x, the value of `f(-2.5)+f(1.5)` is

Options

A. `-2`
B. `1`
C. 1.5
D. 2

Explanation

To solve the problem, we need to evaluate the function \( f(x) = |x| + [x] \) for two values: \( -2.5 \) and \( 1.5 \). Here, \( [x] \) represents the greatest integer less than or equal to \( x \).

### Step 1: Calculate \( f(-2.5) \)
1. **Find \( | -2.5 | \)**:
\[ | -2.5 | = 2.5 \]
2. **Find \( [-2.5] \)**:
The greatest integer less than or equal to \( -2.5 \) is \( -3 \).
\[ [-2.5] = -3 \]
3. **Combine the results**:
\[ f(-2.5) = | -2.5 | + [-2.5] = 2.5 + (-3) = 2.5 - 3 = -0.5 \]

### Step 2: Calculate \( f(1.5) \)
1. **Find \( | 1.5 | \)**:
\[ | 1.5 | = 1.5 \]
2. **Find \( [1.5] \)**:
The greatest integer less than or equal to \( 1.5 \) is \( 1 \).
\[ [1.5] = 1 \]
3. **Combine the results**:
\[ f(1.5) = | 1.5 | + [1.5] = 1.5 + 1 = 2.5 \]

### Step 3: Add the results
Now, we add the two values we calculated:
\[ f(-2.5) + f(1.5) = -0.5 + 2.5 = 2 \]

### Final Answer
The value of \( f(-2.5) + f(1.5) \) is \( \boxed{2} \).

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