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The phrase "a function of only" is correct and usable in written English.
It can be used when specifying that something is determined solely by a particular factor or variable.
Example: "The outcome of the experiment is a function of only the temperature and pressure conditions."
Alternatives: "determined solely by" or "dependent exclusively on".
Exact(57)
Given the epipolar line we can express as a function of only one image coordinates: (4).
As a result, the limit state function is reformulated as a function of only random variables and time.
The degree of damage in a stretched specimen is a function of only the maximum stretch ratio the specimen experienced.
(17) and (18), we can write pressure as a function of only an axial coordinate, that is, p=p z).
This is measured as a function of only one variable: the number of active friends the user has.
These models express that growth and product formation as a function of only biomass with evolution over time.
The refractive index of the AKR wave can be regarded as a function of only in situ electron plasma frequency.
The subproblem is also simplified such that it is a function of only one parameter, and we prove the convexity of the resultant single-variable piecewise optimization problem.
Similar(3)
But understand this: Innovation is not a function of engineering only, but a matter of culture.
Joint time-dependent behaviour was demonstrated by the stiffness and strength degradation as a function of not only temperature but also time.
As results, it is observed that adsorption capacity is a function of not only the TOC but also the SSA.
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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