be a given function

USAGE SUMMARY

The phrase "be a given function" is correct and usable in written English.
It can be used in mathematical or programming contexts to refer to a specific function that is defined or assumed for the purpose of discussion or analysis. Example: "Let f(x) be a given function that represents the relationship between x and y in this equation."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

40 human-written examples

Let (1leqlambda<frac{T-omega_{0}}{eta-omega_{0}}), (hin C ([omega_{0},T]_{q,omega}, {mathbb{R}} )) be a given function, and (varphi: C ([omega_{0},T]_{q,omega }, {mathbb{R}} )rightarrow{mathbb{R}}) be a given functional.

Advances in Difference Equations

Let (alpha,betain 0,1)), (omega>0), (qin 0,1)), (h in C (I_{q,omega}^{T},mathbb{R} )) be a given function, and (phi,psi: C (I_{q,omega}^{T},mathbb{R} )rightarrow mathbb{R}) be given functionals.

Boundary Value Problems

The magnetic reconnection process is initiated by variation of a local resistivity assumed to be a given function of time and spatial coordinates.

Advances in Space Research

Let (xi Etimes Erightarrowmathbb{R}^) be a given function.

Advances in Difference Equations

Let (f Ctimes Crightarrow R) be a given function.

Fixed Point Theory and Applications

Let (f: [0, 1] tomathbb{R}) be a given function.

Advances in Difference Equations

Human-verified similar examples from authoritative sources

Similar Expressions

20 human-written examples

They provide a repertoire of tricks for finding a function whose derivative is a given function.

Encyclopedia Britannica

As for the premise variable we consider three cases where the premise variable is a given function, the output and the state of the underlying system.

Fuzzy Sets and Systems

where ψ ∈ P is a given function.

Boundary Value Problems

where is a given function satisfying (1.9).

Advances in Difference Equations

where is a given function and is an integrable function.

Boundary Value Problems

Expert writing Tips

Best practice

When using "be a given function", ensure the context clearly indicates where the function is defined or previously established. This avoids ambiguity and ensures clarity for the reader.

Common error

Avoid using "be a given function" without providing sufficient context or a clear reference to where the function is defined. Failing to do so can confuse the reader and undermine the technical accuracy of your writing.

Linguistic Context

The phrase "be a given function" typically functions as a declarative statement or introductory clause in mathematical, scientific, and technical writing. It sets the stage for subsequent analysis or discussion by establishing a function as a known or predefined entity, as confirmed by Ludwig.

Expression frequency: Uncommon

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, the phrase "be a given function" is a grammatically correct and accepted expression, mainly used in scientific and technical contexts. Ludwig AI confirms that. It serves to introduce or reference a function that is already defined or assumed to exist. When using this phrase, ensuring that the function's context and definition are clear is crucial to avoid ambiguity. Alternative phrasings like "consider a specified function" or "assume a function is defined" can also be considered based on the specific nuances you wish to convey. The phrase's frequency is uncommon; therefore, prioritize clarity and context when incorporating it into your writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

given the function

Shortened form, directly referencing an already established function.

consider a specified function

Changes the phrasing to emphasize the act of considering a function that has been defined beforehand.

with the function defined as

Specifies that a function's definition is being provided.

consider a function that is predefined

Rephrases the concept to explicitly mention the predefinition of the function.

let's define a function as

Introduces the function definition, shifting the focus to the definition process.

assume a function is defined

Highlights the assumption of a pre-existing function definition.

we define the function as

Emphasizes the action of defining a particular function.

where the function is

Introduces the function within a larger context or equation.

suppose we have a function

Similar to assuming, but frames it as a hypothetical scenario.

let the function be denoted by

Focuses on the notation used for a specific function.

FAQs

How can I use "be a given function" in a sentence?

You can use "be a given function" to introduce a function that is already defined or assumed for a particular context. For instance, "Let f(x) be a given function representing the cost of production."

What's a good alternative to "be a given function"?

Consider using alternatives like "consider a specified function", "assume a function is defined", or "given the function" depending on the context and desired emphasis.

When is it appropriate to use the phrase "be a given function"?

It's suitable in mathematical, scientific, or programming contexts where you need to refer to a function that has been previously defined or is assumed to exist for the purpose of analysis or computation.

Is it always necessary to explicitly define a function when using "be a given function"?

While not always required in every instance, it's best practice to ensure the function's definition is accessible or has been clearly established earlier in the document or discussion to avoid ambiguity.