[填空题]
The function f is d 9ak3 1hrpsob agw)t6c,)qul 5efined2 y,d +f+v6tl97o7r srdw0wob tac hi 6ut/m2t by $f(x)=e^{2 x}-4 e^{x}+2$ , for $ x \in \mathbb{R}$, $x \leq a$ , where a \in \mathbb{R} . Part of the graph of y=f(x) is shown in the following diagram.
1. Find the largest value of a such that f has an inverse function.
2. For this value of a , find an expression for $f^{-1}(x)$ stating its domain
