Discrete Mathematics With Applicat...

5th Edition

EPP + 1 other

ISBN: 9781337694193

Textbook Problem

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Let F and G be functions from the set of all real numbere to itself. Define the product functions F ⋅ G : R → R and G ⋅ F : R → R as follows: For every x ∈ R ,
( F ⋅ G ) ( x ) = F ( x ) ⋅ G ( x ) ( G ⋅ F ) ( x ) = G ( x ) ⋅ F ( x )
Does F ⋅ G = G ⋅ F ? Explain.

To determine

Does F⋅G=G⋅F ? Explain.

Explanation

Given information:

Consider the function F and G are defined from real numbers to itself.

Define the product F⋅G:ℝ→ℝ and G⋅F:ℝ→ℝ for all x∈ℝ as follows.

(F⋅G)(x)=F(x)⋅G(x)(F⋅G)(x)=(G⋅F)(x)

Concept used:

a mod b = remainder

Calculation:

For all real number x∈ℝ

By the definition of F⋅G

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