Suppose that f: R → Rsatisfies f(x + y) = f(x) + f(y) for every , y E R. If f is continuous at some point To € R, prove that there is some constant a E R such that f(ax) = ax for every r E R. f Please note: = ax is GIVEN TO BE CONTINUOUS AND ADDITIVE. What you have to show is s (a.r) = dx Vr €R
Suppose that f: R → Rsatisfies f(x + y) = f(x) + f(y) for every , y E R. If f is continuous at some point To € R, prove that there is some constant a E R such that f(ax) = ax for every r E R. f Please note: = ax is GIVEN TO BE CONTINUOUS AND ADDITIVE. What you have to show is s (a.r) = dx Vr €R
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
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I need to prove there exist some "a" such that f(ax)=ax
Not f(ax)=a f(x)
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