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
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71f37fa2-e158-4ef7-8991-0da70aee8486%2F6b466a1d-f722-4309-b6db-9351542695af%2Fb0ejx36_processed.jpeg&w=3840&q=75)
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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