implicit function
C2technical, academic
Definition
Meaning
In mathematics, a function defined by an equation where the dependent variable is not isolated on one side of the equation; a function whose value is expressed as part of a relationship rather than directly given.
A relationship or dependency that is implied or understood but not directly stated; something that operates or exists as a necessary part of a system or situation without being overtly expressed.
Linguistics
Semantic Notes
In mathematics, 'implicit function' refers to a specific technical concept involving functions defined implicitly by equations (e.g., x² + y² = 1 defines y implicitly as a function of x). In broader usage, the phrase can metaphorically describe something whose nature or operation is understood within a context without explicit declaration.
Dialectal Variation
British vs American Usage
Differences
No significant lexical differences. The mathematical concept is identical. Broader metaphorical use is equally possible in both varieties.
Connotations
Identical technical connotations. In metaphorical use, possibly a slight tendency towards more frequent use in British academic/professional writing, but evidence is weak.
Frequency
Very low frequency in general language; almost exclusively found in technical (mathematical, scientific, economic) contexts. Frequency is equal in UK and US technical registers.
Vocabulary
Collocations
Grammar
Valency Patterns
The implicit function [of + VARIABLE]An implicit function defined by [EQUATION]Treat Y as an implicit function of X.Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “The implicit function of social norms”
- “The body's implicit functions”
Usage
Context Usage
Business
Rare. Might be used metaphorically in economics or game theory: 'Trust acts as an implicit function governing long-term partnerships.'
Academic
Primary context. Standard term in mathematics, calculus, economics, and engineering for functions defined by equations like F(x,y)=0.
Everyday
Extremely rare. Would only be used by someone explaining a technical concept in simple terms.
Technical
Core context. Ubiquitous in advanced mathematics, physics, and engineering texts and discourse.
Examples
By Part of Speech
verb
British English
- We can implicit-function our way to a solution.
- The system is not easily implicit-functioned.
American English
- The relationship allows us to implicit function the variable.
- You cannot simply implicit function that equation.
adverb
British English
- The variable is defined implicit-functionly.
- It behaves implicit-functionly.
American English
- The dependence acts implicit-functionly.
- Solve it implicit-functionly.
adjective
British English
- The implicit-function relationship is complex.
- They used an implicit-function approach.
American English
- We need an implicit function solution.
- This is an implicit function problem.
Examples
By CEFR Level
- This is too hard; it's about maths.
- In maths, sometimes you have an equation where y is not alone; that's an implicit function.
- The circle equation x² + y² = 1 defines y as an implicit function of x at most points.
- Applying the implicit function theorem, we can assert the existence of a differentiable function g(x) near the point where the partial derivative is non-zero.
Learning
Memory Aids
Mnemonic
Imagine a secret code (IMPLICIT) that tells you how to get an answer (FUNCTION) without giving you the direct formula. The rule is hidden inside the relationship.
Conceptual Metaphor
UNDERSTANDING IS SEEING (we 'see' the function implicitly within the equation); A HIDDEN MACHINE (a function that works unseen within a system).
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Не путать с 'подразумеваемая функция' в бытовом смысле (это 'implied function/role'). 'Implicit function' — строгий математический термин: 'неявная функция'.
Common Mistakes
- Using 'implicit function' to mean 'a function that is suggested' in non-technical writing (this is stylistically jarring).
- Confusing 'implicit' with 'explicit' when describing the function type.
- Incorrectly capitalising the term as a proper noun.
Practice
Quiz
What is the primary domain of the term 'implicit function'?
FAQ
Frequently Asked Questions
No. In general English, 'implied function' suggests a role or purpose that is hinted at. 'Implicit function' is a precise mathematical term with a specific definition.
It is a key theorem in calculus and analysis that gives conditions under which an equation of the form F(x,y)=0 defines y as a function of x uniquely and smoothly near a given point.
It is extremely rare and highly metaphorical. It is best avoided in non-technical writing to prevent confusion. Use terms like 'implied role', 'unstated principle', or 'underlying mechanism' instead.
The direct opposite is an 'explicit function', where the dependent variable is given directly in terms of the independent variable(s), e.g., y = x² + 3.