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

Options

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

Answer

To find the value of \( f(-1) \) for the function \( f(x) = \frac{x - |x|}{|x|} \), we will follow these steps:

### Step 1: Substitute \( x = -1 \) into the function
We start by substituting \( -1 \) into the function:
\[ f(-1) = \frac{-1 - |-1|}{|-1|} \]

### Step 2: Calculate \( |-1| \)
Next, we need to find the absolute value of \( -1 \):
\[ |-1| = 1 \]

### Step 3: Substitute the absolute value back into the function
Now, we substitute \( |-1| \) back into the function:
\[ f(-1) = \frac{-1 - 1}{1} \]

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

### Final Answer
Thus, the value of \( f(-1) \) is:
\[ \boxed{-2} \]