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Proof: using the definition of the inverse, and the chain rule.
I'll be taking your grade from your work on-line, while watching your attempts. Important Note: when you need to use the absolute value function, write abs(x) (rather than |x|. You basically input functions just like you would to your TI calculator. I believe that the software checks your answer by comparing it numerically on a bunch of points on a given domain.
(How does symmetry help us to understand the absolute value in this result?)