Let F and G be functions from the set of all real numbers to itself. Define the product
Chapter 7, Problem 15(choose chapter or problem)
Let F and G be functions from the set of all real numbers to itself. Define the product functions \(F \cdot G: \mathbf{R} \rightarrow \mathbf{R}\) and
\(G \cdot F: \mathbf{R} \rightarrow \mathbf{R}\) as follows: For all \(x \in \mathbf{R}\),
\((F \cdot G)(x)=F(x) \cdot G(x)\)
\((G \cdot F)(x)=G(x) \cdot F(x)\)
Does \(F \cdot G=G \cdot F\)? Explain.
Text Transcription:
F cdot G: mathbf R rightarrow mathbf R
G cdot F: mathbf R rightarrow mathbf R
x in mathbf R
(F cdot G)(x)=F(x) cdot G(x)
(G cdot F)(x)=G(x) cdot F(x)
F cdot G=G cdot F
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