Two branches in a reciprocal modulus range

Given \(h(x)=1-|x-2|\), where \(0\le x\le4\), and \(H(x)=\dfrac{1}{h(x)}\), the range of \(H(x)\) is the set \(R\) such that \(R=\{y:y\ge a\text{ or}\hspace{0.5em}y\le b\}\) where \(a,b\in\mathbb Z\).

Determine the values of \(a\) and \(b\), writing your answers in the form \(a,b\).