Question

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

Answer 1

Answer: 1

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