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The phrase "general function" is correct and usable in written English.
You can use it to refer to any broad, overarching purpose or role that something serves. For example, you could say, "The general function of a thermostat is to regulate the temperature of a room."
Exact(60)
We consider generalized Morrey spaces with a general function defining the Morrey-type norm.
Coding for functional ribozymes, at present, cannot be considered a general function of satDNA.
The third general function of the skeleton is that of motion.
True, all of these objects, like their African counterparts, served a general function: in one way or another they were conceived as links between human and spiritual realms.
R General function prediction only.
The general function β may be linear or nonlinear.
The demand is assumed as a general function of price.
The GA general function optimisation software is customised here, to be used as the optimisation tool.
The mode-shape of a cracked beam is first obtained analytically by using a general function.
For more general function case, the reader is referred to Forti [4] and Găvruta [5].
However, the study of problem (1.1) becomes more difficult since M is a general function.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com