Question
Test whether the function, $f(x)=x-\frac{1}{x}, x \in R, x \neq 0$, is increasing or decreasing.
$f(x)=x-\frac{1}{x}, x \in R$
$\therefore f^{\prime}(x)=1-\left(-\frac{1}{x^2}\right)=1+\frac{1}{x^2}$
$\because x \neq 0$, for all values of $x, x^2>0$
$\therefore \frac{1}{ x ^2}>0,1+\frac{1}{ x ^2}$ is always positive
thus f'(x)>o , for all x ∈ R
Hence f(x) is increasing function.
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