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  • Show that the image of the function $f:(0,\infty)\rightarrow \mathbb{R}$, $f(x)=x+\dfrac{1}{x}$ is the interval $[2,\infty)$.

If $x=1$, then $f(1)=2$. So how can I show that the mage of the function is the interval $[2,\infty)$?