Question

The domain of the function \(f(x)=\frac{1}{\sqrt{|x|-x}}\) is

• A. \((0,\infty )\)
• B. \((-\infty ,0)\)
• C. \((-\infty ,\infty )-\{0\}\)
• D. \((-\infty ,\infty )\)

Hint:

The expression under the root must be strictly positive.

Answer 1

The Correct Option is B

Step 1: Rewrite
$|x|-x$ equals $0$ for $x\ge 0$ and $-2x$ for $x\lt 0$.

Step 2: Condition
We need a positive value, which occurs only when $x\lt 0$.

Step 3: Conclusion
Domain $= (-\infty ,0)$.

Final Answer:
The function is defined only for negative x. \[ \boxed{\text{(B) }(-\infty ,0)} \]