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Theorem 12. Let f be a non-zero continuous function on R such that f(x+y)=f(x) f(y) ¥x, yER. Show that f(x)3ec*, for some constant c#0.

Theorem 12. Let f be a non-zero continuous function on R such that f(x+y)=f(x) f(y) ¥x, yER. Show that f(x)3ec*, for some constant c#0.

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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Theorem 12. Let f be a non-zero continuous function on R such that f(x+y)=f(x) f(y) ¥x, yER. Show that f(x)=ec*, for some constant c±0.
Transcribed Image Text:Theorem 12. Let f be a non-zero continuous function on R such that f(x+y)=f(x) f(y) ¥x, yER. Show that f(x)=ec*, for some constant c±0.
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