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7.1 Example: Equality of Functions a. Let J 0,,2}, and define functions fand g from J to J as follows: For all x in J3, f (x) = (x2 +x 1) mod 3 g(x) = (x + 2)? mod 3. and Does f g? b. Let F: R R and G: R -R be functions. Define new functions F G: R -» R and G + F: R -»R as follows: For all x e R (F G)(x) F(x) + G(x) and (G+ F)(x)= G(x) F(x) Does F G G + F?

7.1 Example: Equality of Functions a. Let J 0,,2}, and define functions fand g from J to J as follows: For all x in J3, f (x) = (x2 +x 1) mod 3 g(x) = (x + 2)? mod 3. and Does f g? b. Let F: R R and G: R -R be functions. Define new functions F G: R -» R and G + F: R -»R as follows: For all x e R (F G)(x) F(x) + G(x) and (G+ F)(x)= G(x) F(x) Does F G G + F?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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7.1 Example: Equality of Functions a. Let J 0,,2}, and define functions fand g from J to J as follows: For all x in J3, f (x) = (x2 +x 1) mod 3 g(x) = (x + 2)? mod 3. and Does f g? b. Let F: R R and G: R -R be functions. Define new functions F G: R -» R and G + F: R -»R as follows: For all x e R (F G)(x) F(x) + G(x) and (G+ F)(x)= G(x) F(x) Does F G G + F?
Transcribed Image Text:7.1 Example: Equality of Functions a. Let J 0,,2}, and define functions fand g from J to J as follows: For all x in J3, f (x) = (x2 +x 1) mod 3 g(x) = (x + 2)? mod 3. and Does f g? b. Let F: R R and G: R -R be functions. Define new functions F G: R -» R and G + F: R -»R as follows: For all x e R (F G)(x) F(x) + G(x) and (G+ F)(x)= G(x) F(x) Does F G G + F?
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