Given n e N and the function f : R" → R", we can define, for each nonnegative integer k, the kth iterate fk of f as follows: first let fº be the identity map on R", and then for each k > 0 let fk+1 = f o fk. If ƒ is linear, must fk necessarily be linear for all k? Prove your claim.
Given n e N and the function f : R" → R", we can define, for each nonnegative integer k, the kth iterate fk of f as follows: first let fº be the identity map on R", and then for each k > 0 let fk+1 = f o fk. If ƒ is linear, must fk necessarily be linear for all k? Prove your claim.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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