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Suppose that S is a vector space that is a subspace of the space of functions from R to R. Furthermore suppose that every element of S is a polynomial function, and that if p is in S then p(5)=k, where k is some constant. What must the value of k be equal to and why?

Suppose that S is a vector space that is a subspace of the space of functions from R to R. Furthermore suppose that every element of S is a polynomial function, and that if p is in S then p(5)=k, where k is some constant. What must the value of k be equal to and why?

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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Suppose that S is a vector space that is a subspace of the space of functions from R to R. Furthermore suppose that every element of S is a polynomial function, and that if p is in S then p(5)=k, where k is some constant. What must the value of k be equal to and why?
Transcribed Image Text:Suppose that S is a vector space that is a subspace of the space of functions from R to R. Furthermore suppose that every element of S is a polynomial function, and that if p is in S then p(5)=k, where k is some constant. What must the value of k be equal to and why?
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