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The graph given is very close to this (which I believe is close enough for this question): http://www.math.unl.edu/~bharbour/M106/projects/grphI1.gif

I believe the inverse of this function is basically this graph rotated 45 degrees to the right, as if you plot the inverse points (i.e. (8, 10) instead of (10, 8), etc you end up with this. Am I correct in thinking this?

My problem is that I am not sure what the inverse represents as it doesn't make a lot of sense to me (which is one reason I think I may have the inverse totally wrong). I think the inverse would no longer be a function because many pairs have multiple Y values per X. Also the graph gives odd results such as (135 days have 24 hours of daylight), so I am obviously missing some concept.

Thanks for any help.