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passing functions as parameters


How would one pass one function to another?

I need to be able to define functions in the following fashion:

f[x_]:=x^3-x+1

g[x_,y_,somefunction?]:=If[somefunction[x]>somefunction[y],"Done","Waiting")

to be able to later on evaluate

g[2.,3., f?]

I have tried couple of paths with no success and would really like to
avoid using global function in function g.

All the best...



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