Question

If \(A\) and \(B\) are the domain and range of the real valued function, \[ f(x)=\dfrac{|x|}{\sqrt{1-|x|}} \] then \(A \cup B =\ ?\) 

• A. \((1,\infty)\)
• B. \([0,\infty)\)
• C. \((-1,\infty)\)
• D. \(\mathbb{R}\) \bigskip

Hint:

For functions containing square roots in the denominator, always use the condition \[ \text{Radicand}>0 \] instead of merely \(\ge0\). This helps determine the exact domain correctly.

Answer 1

The Correct Option is C