Question

Test whether the function, $f\left(x\right)=x-\frac{1}{x},xϵR,x\ne 0$, is increasing or decreasing

Answer 1

Given function is $f\left(x\right)=x-\frac{1}{x}$ and $x\ne 0$ , $x\in R$

Now differentiate the given function , we get $f^1\left(x\right)=1+\frac{1}{x^2}$

For $x\in R$ and $x\ne 0$ , $1+\frac{1}{x^2}>0$

Therefore $f^1\left(x\right)$ is always greater than zero for all $x\in R$ and $x\ne 0$

So the function $f\left(x\right)$ is increasing function in the given domain