Help analyzing inverse of an abs function
I am trying to find an expression for
And then the algebra
I think my calculator is telling me that the first solution I did is true for and and the second solution is true for all reals.
If I am understanding my calculator correctly, how do I analytically determine that the second solution is the inverse of f for all real values of x? And if this is incorrect, how do I analyze the functions I found for ?
Thanks a lot if you can help!