2. Given the function $f(x)=\left\{\begin{array}{l}2^{-x}-1,(x \leqslant 0), \\ f(x-1),(x>0),\end{array}\right.$ If the equation $f(x)=x+a$ has exactly two distinct real roots, then the range of the real number $a$ is $\qquad$ .
2. Solution: Combination of number and shape. $(-\infty, 1)$