An element of $C(\mathbb{D})$ which is not in the connected component

Question

Let $\mathbb{\bar{D}}$ denote the closed unit disc in the complex plane. Let $A=C(\mathbb{\bar{D}})$ be the Banach algebra of all complex valued continuous functions on $\mathbb{\bar{D}}$. My Question is with regard to this mathoverflow question. Let $G(A)$ denote the set of all invertible elements in $A$ and let $G_1(A)$ denote the connected component of $G(A)$ containing the identity element. Can you give an example of an element $f\in A$ such that $f\in G(A)\setminus G_1(A)$?