Function right-arrow notation in Wolfram|Alpha?

Questions
1

I was not sure what exactly to search to find more information on this, but I’m totally lost when it comes to this notation:

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with the right facing arrow. Copying the text just refers to the symbol as “function”. I’ve seen this come up on lots of differential equation solutions (I was solving y’‘=-sgn(y’) for this one) but I can’t seem to figure out what it actually means. Is anyone able to provide a little insight into this?
Thanks!

2

In this context, (x ⟼ f(x))⁽⁻¹⁾ means ‘the inverse of f’, that is, f⁽⁻¹⁾. It is being evaluated at c₁-ζ. The inverse of that integral is, probably, quite complicated and has no nice formula.

3

Thank you so much! That makes a lot more sense