Prove that function f ( x )=x-1 x , x R and x 0 is increasing fun… - Vidyadip

Question

Prove that function $f ( x )=x-\frac{1}{x}, x \in R$ and $x \neq 0$ is increasing function

✓

Answer

$ f ( x )=x-\frac{1}{x}, x \in R , x \neq 0$
$\therefore f ^{\prime}( x )=1+\frac{1}{x^2} $
$x^2$ is always positive for $x \neq 0$
$\therefore f ^{\prime}( x )>0$ for all $x \in R , x \neq 0$
Hence, $f(x)$ is an increasing function for all $x \in R, x \neq 0$.

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