3.3.4. Suppose that f and g are different constant functions from S to S. Show that ƒ og + gof. Proof. Since f and g are different constant functions, there exists distinct elements ES and E S such that f(x) = and g(x) : x € S. Then (ƒ o g)(x) = for and (gof)(x) = for x E S. This implies fog + gof.
3.3.4. Suppose that f and g are different constant functions from S to S. Show that ƒ og + gof. Proof. Since f and g are different constant functions, there exists distinct elements ES and E S such that f(x) = and g(x) : x € S. Then (ƒ o g)(x) = for and (gof)(x) = for x E S. This implies fog + gof.
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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Transcribed Image Text:3.3.4. Suppose that f and g are different constant functions from S to S. Show that ƒ og + gof.
Proof. Since f and g are different constant functions, there exists distinct elements
ES and
E S such that f(x) =
and g(x) :
x € S. Then (ƒ o g)(x) =
for
and (gof)(x) =
for
x E S. This implies fog + gof.
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