Your idea is strange. This is a piecewise function. Of course, we should consider it separately. This is not a monotonous function. You can't use it like this. The solution to the problem is as follows:

First of all, when we look at this function, we find that both segments pass through the fixed point (1, 1) and there is no monotonicity.

For the binary linear equation, the opening of the function is upward, and it can be judged that there are no two solutions by finding the root, that is, △≤0, and the range of a value of the solution is [0,2];

For the second function, it is judged that the minimum value is X = A. From the above, A holds when [0, 1], and the minimum value needs to be greater than or equal to 0 when A is [1, 2], that is, the value range of A is [1, e] when a-alna≥0.