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

Answer

To find \( f(-1) \) 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 this value back into our function:
\[ f(-1) = \frac{-1 - 1}{1} \]

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

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

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

---