Question
$f(x)=x-\frac{1}{x}, x \in R, x \neq 0$

Answer

$
\begin{aligned}
& f(x)=x-\frac{1}{x} \\
& \therefore f^{\prime}(x)=\frac{d}{d x}\left(x-\frac{1}{x}\right) \\
& =1-\left(-\frac{1}{x^2}\right) \\
& =1+\frac{1}{x^2}>0 \text { for all } x \in R , x \neq 0
\end{aligned}
$
$\therefore f ^{\prime}( x )>0$ for all $x \in R$, where $x \neq 0$
$\therefore f$ is increasing for all $x > R$, where $x \neq 0$.

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