PP form for the reverse function (not inverse function)

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Hello friends!
Consider a pp form for a set of (x,y) data points. Imagine now that we wish to find the pp form for the (x,1/y) data
points using the pp form for the (x,y) data. I am wondering whether matlab has a function which can calculate this?
Of course, I can simply calculate it indirectly but I am not sure if this is the best way to perform such a calculation
in terms of both speed and acuracy. For instance, the following do the job for the function cos(x) over [-pi/2 pi/2]:
I seriously doubt whther my approach is efficient? (I feel not)
Any idea?
Thanks in advance!

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