We denote by $\mathcal{E}$ the set of continuous maps $g$ from $[0,1]$ to $\mathbf{C}$ such that $g(0)=-1$ and $g(1)=1$. Determine the unique element $f_0$ of $\mathcal{E}$ which is affine.
We denote by $\mathcal{E}$ the set of continuous maps $g$ from $[0,1]$ to $\mathbf{C}$ such that $g(0)=-1$ and $g(1)=1$.
Determine the unique element $f_0$ of $\mathcal{E}$ which is affine.