Is every function an explicit function?

No. Many functions are defined implicitly. A function is only explicit if it is written in the form y = f(x) (or similar), with the output variable alone on one side.

Can any implicit function be converted to an explicit function?

Not always. While sometimes possible algebraically (e.g., solving for y), many implicit relations either define multiple explicit functions (e.g., a circle) or cannot be solved into a single, simple explicit formula.

Does 'explicit' in 'explicit function' mean the same as in 'explicit language'?

The core idea of being 'clearly expressed and leaving nothing implied' is related. In mathematics, it is narrowly technical (isolated variable). In general language, it means 'stated clearly and in detail,' often with a connotation of graphic or blunt detail.

Why are explicit functions important?

They allow for direct evaluation, graphing, differentiation, and integration using standard rules. They make the input-output relationship transparent and computationally straightforward.

explicit function

Low in general English; very high in academic/mathematical contexts.

UK/ɪkˈsplɪsɪt ˈfʌŋkʃən/US/ɪkˈsplɪsɪt ˈfʌŋkʃən/

Formal, academic, technical.

My Flashcards

Definition

Meaning

In mathematics, a function expressed directly as one variable (usually the dependent variable) in terms of other variables (usually independent variables). Formally, of the form y = f(x₁, x₂, ...).

Outside strict mathematics, can refer to any process, rule, or relationship that is clearly and unambiguously stated, defined, or formulated, leaving no room for interpretation.

Linguistics

Semantic Notes

The term inherently contrasts with 'implicit function.' It emphasizes clarity, direct expression, and the absence of hidden steps or ambiguity in definition.

Dialectal Variation

British vs American Usage

Differences

No significant differences in meaning or usage. Spelling conventions for related words (e.g., 'mathematical' vs. 'mathematics') may follow regional norms.

Connotations

Identical technical connotations. In non-technical extended use, carries the same force of unambiguous clarity in both dialects.

Frequency

Equally common in both British and American academic mathematical discourse.

Vocabulary

Collocations

strong

define an explicit functionwrite as an explicit functionexpress... explicitlyexplicit function ofexplicit functional form

medium

solve for an explicit functiongiven by an explicit functionexplicit function representation

weak

find the explicit functionexplicit function definitionexplicit function is preferred

Grammar

Valency Patterns

[NP] is/gives/provides an explicit function of [NP]to express [NP] as an explicit function of [NP]

Vocabulary

Synonyms

Strong

explicit formexplicit expression

Neutral

directly expressed functionclosed-form expressionexplicit formula

Weak

solved functiondefined function

Vocabulary

Antonyms

implicit functionimplicit relationimplicit definition

Phrases

Idioms & Phrases

“None for this technical term.”

Usage

Context Usage

Business

Virtually never used. If used, it would be a metaphorical extension, e.g., 'We need an explicit function for calculating bonuses, not managerial discretion.'

Academic

Primary domain. Ubiquitous in mathematics, physics, engineering, and economics texts to describe relationships where the dependent variable is isolated.

Everyday

Extremely rare. Would sound highly technical and out of place.

Technical

Core term in calculus, analysis, and mathematical modelling. Precisely defined and used with formal rigor.

Examples

By Part of Speech

adverb

British English

The rule was stated explicitly in the contract.

American English

She explicitly forbade any further discussion.

adjective

British English

The relationship is not explicit.
We require an explicit definition.

American English

The instructions were not explicit enough.
He gave explicit consent.

Examples

By CEFR Level

In algebra, we often rewrite equations to get an explicit function, like y = 2x + 1.
The textbook asked us to find an explicit function for the relationship.

The solution to the differential equation yielded an explicit function for population growth over time.
Unlike the implicit relation F(x,y)=0, an explicit function y=f(x) is far more convenient for computation.

Learning

Memory Aids

Mnemonic

Think: 'EX-PLI-CIT' = 'EX-Plained CLEARly and speCIFICally In Terms (of the independent variable).'

Conceptual Metaphor

CLARITY IS VISIBILITY / A MACHINE WITH EXPOSED WORKINGS. An explicit function is like a vending machine with a clear glass front—you can see exactly which button (input) leads to which snack (output).

Watch out

Common Pitfalls

Translation Traps (for Russian speakers)

Do not confuse with просто 'explicit' (явный, откровенный). The mathematical term is consistently translated as 'явная функция'.
Avoid using 'чёткая функция' (clear function) or 'определённая функция' (definite function) for this concept; they do not carry the specific mathematical meaning.

Common Mistakes

Confusing 'explicit function' with 'explicit content'.
Using 'explicit' as a general intensifier (e.g., 'explicitly difficult function').
Misspelling as 'explicite function'.
Failing to contrast it properly with 'implicit function'.

Practice

Quiz

Fill in the gap

In calculus, it is often easier to work with an function, such as y = sin(x), rather than an implicit one like x² + y² = 1.

Multiple Choice

What is the defining characteristic of an explicit function?

FAQ

Frequently Asked Questions

: No. Many functions are defined implicitly. A function is only explicit if it is written in the form y = f(x) (or similar), with the output variable alone on one side.
: Not always. While sometimes possible algebraically (e.g., solving for y), many implicit relations either define multiple explicit functions (e.g., a circle) or cannot be solved into a single, simple explicit formula.
: The core idea of being 'clearly expressed and leaving nothing implied' is related. In mathematics, it is narrowly technical (isolated variable). In general language, it means 'stated clearly and in detail,' often with a connotation of graphic or blunt detail.
: They allow for direct evaluation, graphing, differentiation, and integration using standard rules. They make the input-output relationship transparent and computationally straightforward.