If `f(x)=(x-|x|)/(|x|),` then `f(-1)=`

Options

A. 1
B. `-2`
C. 0
D. 2

Answer

To solve the problem, we need to evaluate the function \( f(x) = \frac{x - |x|}{|x|} \) at \( x = -1 \).

### Step-by-step Solution:

1. **Identify the function**:
We have \( f(x) = \frac{x - |x|}{|x|} \).

2. **Substitute \( x = -1 \)**:
We need to find \( f(-1) \). So we substitute \( -1 \) into the function:
\[ f(-1) = \frac{-1 - |-1|}{|-1|} \]

3. **Calculate the absolute value**:
The absolute value \( |-1| \) is \( 1 \). Therefore, we can rewrite the function:
\[ f(-1) = \frac{-1 - 1}{1} \]

4. **Simplify the expression**:
Now, we simplify the numerator:
\[ f(-1) = \frac{-2}{1} \]

5. **Final result**:
Thus, we find:
\[ f(-1) = -2 \]

### Conclusion:
The value of \( f(-1) \) is \( -2 \).