The domain of the function
`f(x) =(1)/(sqrt(|x|-x))`, is

Options

A. `(0,oo)`
B. `(-oo,0)`
C. `R-{0}`
D. none of these

Explanation

To find the domain of the function \( f(x) = \frac{1}{\sqrt{|x| - x}} \), we need to ensure that the expression under the square root is positive, as well as ensure that the denominator is not zero.

### Step 1: Analyze the expression under the square root
The expression under the square root is \( |x| - x \).

### Step 2: Determine when \( |x| - x > 0 \)
We need to find when \( |x| - x > 0 \).

#### Case 1: \( x \geq 0 \)
If \( x \geq 0 \), then \( |x| = x \). Therefore:
\[ |x| - x = x - x = 0 \]
This does not satisfy our condition since we need it to be greater than zero.

#### Case 2: \( x < 0 \)
If \( x < 0 \), then \( |x| = -x \). Therefore:
\[ |x| - x = -x - x = -2x \]
Now we need to check when:
\[ -2x > 0 \implies x < 0 \]
This is always true for \( x < 0 \).

### Step 3: Combine the conditions
From our analysis:
- For \( x \geq 0 \), \( |x| - x = 0 \) which is not allowed.
- For \( x < 0 \), \( |x| - x > 0 \).

Thus, the function is defined only for \( x < 0 \).

### Conclusion
The domain of the function \( f(x) = \frac{1}{\sqrt{|x| - x}} \) is:
\[ (-\infty, 0) \]