Question

The domain of \(f(x)=\sqrt{\left(\frac{1}{\sqrt{x}}-\sqrt{x+1}\right)}\) is
(A) \(x>-1\)
(B) \((-1, \infty) \backslash\{0\}\)
(C) \(\left(0, \frac{\sqrt{5}-1}{2}\right]\)
(D) \(\left[\frac{1-\sqrt{5}}{2}, 0\right)\)

Answer 1

Ans: (C)
Hint : \(x^{2}+x-1 \leq\) and \(x>0\)
$$
\begin{aligned}
&x \in\left[\frac{-1-\sqrt{5}}{2}, \frac{\sqrt{5}-1}{2}\right] \\
&x \in\left(0, \frac{\sqrt{5}-1}{2}\right]
\end{aligned}
$$