WBJEE · Maths · Functions
The domain of \(f(x)=\sqrt{\left(\frac{1}{\sqrt{x}}-\sqrt{x+1}\right)}\) is
- A \(x>-1\)
- B \((-1, \infty)\) K \(\{0\}\)
- C \(\left(0, \frac{\sqrt{5}-1}{2}\right]\)
- D \(\left[\frac{1-\sqrt{5}}{2}, 0\right)\)
Answer & Solution
Correct Answer
(C) \(\left(0, \frac{\sqrt{5}-1}{2}\right]\)
Step-by-step Solution
Detailed explanation
Hint: \(x^{2}+x \leq 1\) and \(x>0\) \(x \in\left[\frac{-1-\sqrt{5}}{2}, \frac{\sqrt{5}-1}{2}\right]\) \(x \in\left(0, \frac{\sqrt{5}-1}{2}\right]\)
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