Question:
Show that $f(x)=\frac{1}{x}$ is a decreasing function on $(0, \infty)$.
Solution:
we have
$\mathrm{f}(\mathrm{x})=\frac{1}{\mathrm{x}}$
let $x_{1}, x_{2} \in(0, \infty)$ We have, $x_{1}>x_{2}$
$\Rightarrow \frac{1}{x_{1}}<\frac{1}{x_{2}}$
$\Rightarrow f\left(x_{1}\right) Hence, $x_{1}>x_{2} \Rightarrow f\left(x_{1}\right) So, $f(x)$ is decreasing function
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