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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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