Let $f:[a,b]\rightarrow[f(a),f(b)]$ be strictly increasing continuous function (i.e $x>y \implies f(x)>f(y)$). Prove that f is invertible.
Proving that the function is one-to-one was simple enough. I need some guidance on proving it's onto. I'm new to $\epsilon-\delta$ proofs since I just started self-studying some metric spaces.