Prove $x<\sqrt{x^2+1}$.
I am pretty sure this an easy question as the inequality seems obviously true, but I am not entirely convinced by my argument.
So I squared both sides (is this allowed?):
$x^2<x^2+1$, so $0<1$ so the inequality is obviously true.
However, I am unconvinced that this process is reversible due to the squaring, so could someone just explain whether this is correct?