The most common and most likely answer to this crossword clue is the 8 letter word CALCULUS
I've seen this crossword clue in The Guardian
C
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Buddy explains!

The straight part
We know that "Functional study" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case functional study = calculus.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CALCULUS mean?
CALCULUS noun- Calculation; computation.
- Any formal system in which symbolic expressions are manipulated according to fixed rules.
- (often definite, the calculus) Differential calculus and integral calculus considered as a single subject; analysis.
- A stony concretion that forms in a bodily organ.
- Deposits of calcium phosphate salts on teeth.
- A decision-making method, especially one appropriate for a specialised realm.