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The phrase "a function is given" is correct and usable in written English.
It can be used in mathematical or programming contexts to indicate that a specific function has been provided for analysis or use.
Example: "In this problem, a function is given that describes the relationship between the variables."
Alternatives: "a function is provided" or "a function is specified".
Exact(8)
Assume that a function is given by (2.6).
where is the linear diffusion operator whose action on a function is given by (26).
The Riemann-Liouville fractional primitive of order of a function is given by (2.1).
The Riemann-Liouville fractional integral of order of a function is given by (2.1).
The Riemman-Liouville fractional integral of order of a function is given by (2.1).
The fractional integral of order of a function is given by (2.1).
Similar(52)
Let a function be given.
Let and a function be given.
The Riemann-Liouville, the Grünwald-Letnikov, and the Caputo definitions of a fractional derivative of a function are given by (2.1).
When strong support for a function was given for closely related sequences, we modified the existing annotation for some genes.
Hypothetical genes lacking a function were given a putative function using interaction data from yeast two hybrids (provided on PlasmoDB) [ 33] and PlasmoMAP http://www.cbil.upenn.edu/plasmoMAP/index-v1.html[ 34].
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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