Finding the Norm of an Element

Finding the Norm of an Element

This may sound very trivial, but I do not know what I am missing.
Take $X$ be the space of complex valued continuous functions on $[0,1]$
with the usual sup norm. Take $Y=\{f \in C[0,1]:f(0)=0\}$.
Show that:
$Y$ is closed in $X$
$X/Y$ is isomorphic to the set of complex numbers $\mathbb{C}$.
Consider the quotient space $X/Y$ with the usual quotient norm. Let us
denote the elements of $X/Y$ by $[x]$. Show that $||[f]||=|f(0)|$.
I have done 1 and 2, but unable to do 3.
Thanks for any help.