Solve Preimage Function & Find x-1=e^-x Solution [-2,2]

[shrody]

1.My first problem revolves around the preimage of a function. I have never truly understood this concept, if anyone can clear this with a simple example I would appreciate it.
2.Does x-1=e^-x a solution in the interval [-2, 2] have?

 

[HallsofIvy]

German? You are putting all your verbs at the end of the sentence!

It's pretty easy to see, isn't it, that when x= 0 x-1= -1 and $e^{-x}= e^{-1}> -1 while if x= 2, x-1= 1 and e^{-2}= .1356< 1.$