Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Find the number of integers lying in the domain of the function $f(x)=\sqrt{\log _{(0.5)}\left(\frac{5-2 x}{x}\right)}$ is

NTA AbhyasNTA Abhyas 2022

Solution:

We have, $f(x)=\sqrt{\log _{0.5}\left(\frac{5-2 x }{ x }\right)}$
Now, $\log _{0.5}\left(\frac{5-2 x}{x}\right) \geq 0$
$ \begin{array}{l} \Rightarrow 0<\frac{5-2 x}{x} \leq 1 \\ \Rightarrow x \in\left[\frac{5}{3}, \frac{5}{2}\right) \end{array} $