Finding the domain of the inverse function

[System]

Homework Statement

Let f(x)=e^(-x)-x ,, x belongs to R

Find the domain of f inverse

Homework Equations

Domain of f inverse = range of f

The Attempt at a Solution

we have :

-inf < x < inf
-inf < -x < inf ... (1)
0 < e^(-x) < inf ... (2)

By adding (1) and (2) :

-inf < e^(-x) - x < inf

So domain of f = R = range of f inverse.

Is this correct?

Can I add the inequalities together?

 

[Raskolnikov]

Ignore my last post. I read the function wrong. Yep, the domain of the inverse is all real numbers.

 

[System]

Thanks.