composition of functions

USAGE SUMMARY

The phrase "composition of functions" is correct and usable in written English.
It is typically used in mathematics to describe the process of combining two functions where the output of one function becomes the input of another. Example: "In calculus, the composition of functions allows us to evaluate complex expressions more efficiently, such as f(g(x))."

✓ Grammatically correct

Science

Academia

Human-verified examples from authoritative sources

Exact Expressions

9 human-written examples

We can always transform a network of actors into a composite actor with feedback, where the function of the composition actor is the composition of functions of the component actors.

University of California, Berkeley

Many conceptual difficulties that have been reported in the research literature were not as prevalent for our participants and some of them were capable of solving difficult problems involving composition of functions.

The Journal of Mathematical Behavior

Here, ∘denotes the composition of functions.

EURASIP Journal on Advances in Signal Processing

The union of automorphisms and anti-automorphisms also form a group under the composition of functions.

Fixed Point Theory and Applications

Using the theorem of composition of functions of (see [13]) it is easy to see that.

Boundary Value Problems

where ∘ represents the composition of functions, Φ k|k−1 is the prediction operator, and Ψ k is the update operator.

EURASIP Journal on Advances in Signal Processing

Human-verified similar examples from authoritative sources

Similar Expressions

51 human-written examples

Meanwhile, the composition of function categories in ArathMitoP set and GSP dataset are also illustrated in Fig. 4. ArathMitoP set contains 2,311 integrated mitochondrial proteins from fourteen genome-wide predictors and the assembled CoreMitoP contains 2,585 potential mitochondrial proteins.

Plosone

Imaging pipelines are compositions of functions.

Stanford University

First of all, compositions of functions like sin sin(x)) are remarkably sparse in physics.

Harvard University

We consider nonsmooth multiobjective programs where the objective function is a fractional composition of invex functions and locally Lipschitz and Gâteaux differentiable functions.

Journal of Inequalities and Applications

In neural networks, the function f(x) is composition of other functions g i (x) which are also composition of other functions like a network structure with non-linear weighted sum as the type of composition in general, ({f}(mathbf {x})=mathbf {K}left (sum _{i}{w_{i}}{g_{i}}(mathbf {x} right)), K is an activation function.

EURASIP Journal on Advances in Signal Processing

Expert writing Tips

Best practice

When writing about mathematical concepts, ensure that the term "composition of functions" is used in its correct context, referring to the application of one function to the result of another. Using clear notation and providing examples can enhance understanding.

Common error

A common error is to reverse the order of functions in a "composition of functions". Remember that in f(g(x)), g(x) is applied first, and then f is applied to the result. Always clarify the sequence to avoid misinterpretations.

Linguistic Context

The phrase "composition of functions" functions as a noun phrase that denotes a mathematical operation. As evidenced by Ludwig AI, it is typically used in contexts related to mathematical and computational sciences to describe the process of combining two or more functions.

Expression frequency: Uncommon

Frequent in

Science

60%

Academia

30%

Wiki

10%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, "composition of functions" is a noun phrase that refers to the mathematical operation of applying one function to the result of another. Ludwig AI indicates that this phrase is grammatically correct and most frequently used in scientific and academic contexts. Key to its correct usage is understanding the order of operations, ensuring that the inner function is evaluated before the outer one. Related terms include "function composition" and "composite function". While not as common as other mathematical terms, mastering the use of "composition of functions" is essential for clarity and precision in mathematical and scientific writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

function composition

Reorders the words while retaining the core meaning.

composite function

Uses an adjective to describe the type of function.

function combination

Replaces 'composition' with 'combination' to emphasize the act of combining.

application of functions

Focuses on the action of applying one function after another.

functional composition

Adjectival form, emphasizing the compositional aspect.

chaining of functions

Uses 'chaining' to represent the sequential nature of the process.

function layering

Implies a layered structure where one function operates on another.

iterated function

Describes repeated application, a specific type of composition.

nested function

Highlights the nesting aspect of one function within another.

sequential function application

Emphasizes the order of applying functions.

FAQs

What is "composition of functions" in simple terms?

It's like a machine where you put something in, and then the output goes into another machine. In math, it means applying one function to the result of another, like f(g(x)).

How do I evaluate the "composition of functions"?

To evaluate f(g(x)), first find g(x), then substitute that result into f(x). For example, if f(x) = x + 1 and g(x) = x^2, then f(g(x)) = x^2 + 1.

What are some synonyms for "composition of functions"?

Alternatives include "function composition", "composite function", or "function combination". The best choice depends on the specific context.

How is "composition of functions" different from multiplying functions?

The "composition of functions", f(g(x)), means applying g first, then f. Multiplying functions, f(x) * g(x), means multiplying the outputs of f(x) and g(x) separately.