Question

Is $(f \circ g)(x)=(g \circ f)(x)$ for all values of $x$ ? Explain and give an example to support your answer.

Name: Problem 95, Chapter 9: Intermediate Algebra for College Students
Uploaded: 2020-05-20T15:59:12-08:00
Duration: 2 min 21 s
Channel: Kevin Harmer
Description: Is (f ∘g)(x)=(g ∘f)(x) for all values of x ? Explain and give an example to support your answer.

   Is $(f \circ g)(x)=(g \circ f)(x)$ for all values of $x$ ? Explain and give an example to support your answer.

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 9, Problem 95

Instant Answer

Solved by Expert Kevin Harmer

05/20/2020

Step 1

In order for these two expressions to be equal for all values of $x$, it must be the case that applying the function $g$ first and then applying the function $f$ gives the same result as applying the function $f$ first and then applying the function $g$. This is Show more…

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Is $(f \circ g)(x)=(g \circ f)(x)$ for all values of $x$ ? Explain and give an example to support your answer.

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Key Concepts

Function Composition

Function composition is the process of applying one function to the results of another, denoted by f(g(x)) or g(f(x)). This operation involves taking the output from one function as the input to another, and the order in which the functions are applied is crucial as it determines the overall outcome.

Commutativity in Operations

The concept of commutativity refers to the property where changing the order of the operations does not change the result. In the context of function composition, however, this property generally does not hold. That is, f(g(x)) is not necessarily equal to g(f(x)) for all x because the effect of applying one function before the other can yield different outcomes unless specific conditions or special functions are used.

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