mathschallenge.net

Problem

Consider the function, $f(x) = x + \dfrac{1}{x}$.

$f(2) = 2 + \dfrac{1}{2} = 2.5$
$f(0.4) = 0.4 + \dfrac{1}{0.4} = 2.9$
$f(1.25) = 1.25 + \dfrac{1}{1.25} = 2.05$

Prove that $f(x) \ge 2$ for all real values of $x \gt 0$.