Question

The range of the function $f\left(x\right)=x+\frac{1}{x}$ is

Answer 1

$x+\frac{1}{x}\ge 2\sqrt{x-\frac{1}{x}}$

$x+\frac{1}{x}\ge 2$

Range $\in (2,\infty )$ for $x>0$

for $x<0$

$x+\frac{1}{x}\le -2\sqrt{x.\frac{1}{x}}=-2$

Range of $+\left(x\right)=(-\infty ,-2]u[2,\infty )$