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The phrase "a unique function" is correct and usable in written English.
It can be used when describing a specific role or purpose that is distinct and not replicated by others.
Example: "The software has a unique function that allows users to customize their experience based on individual preferences."
Alternatives: "a distinct role" or "a singular purpose".
Exact(57)
American higher education performs a unique function.
He realizes that each vector bears a unique function.
Regulation of antifreeze protein production in winter flounder: A unique function for growth hormone.
As a unique function apart from CSR, many large corporations maintain foundations.
Both experiments as well as theory indicate velocity to be a unique function of annulus dimension.
Representing productions at particular time for different permeability distributions requires a unique function.
H1.1 shows a DamID binding profile distinct from the other subtypes, suggesting a unique function.
The disk golfer even carries a bag with a wide assortment of disks, or "clubs," each of which serves a unique function.
Similar(3)
And the large macrosatellite array DXZ4 appears to have a unique function in the process of X chromosome inactivation [ 13].
Then there exists a unique function such that (3.9).
If assumption (H) holds and is piecewise -expansive, then there exists a unique function satisfying (1.1) and condition (2.18).
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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