2. Let V be the (real) vector space of all functions f from R into R. Which of the following sets of functions are subspaces of V? etf Won (a) all f such that f(x) = f(x)2; (b) all f such that f(0) = f(1); (c) all f such that f(3) = 1+ f(-5); (d) all f such that f(-1) = 0; (e) all f which are continuous. oldetive a bnd deum ow lasin shob ed fliw aidT aoaqe 1otoov VIOPonep me mansA ad V i olsiail
2. Let V be the (real) vector space of all functions f from R into R. Which of the following sets of functions are subspaces of V? etf Won (a) all f such that f(x) = f(x)2; (b) all f such that f(0) = f(1); (c) all f such that f(3) = 1+ f(-5); (d) all f such that f(-1) = 0; (e) all f which are continuous. oldetive a bnd deum ow lasin shob ed fliw aidT aoaqe 1otoov VIOPonep me mansA ad V i olsiail
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:2. Let V be the (real) vector space of all functions f from R into R. Which of the
following sets of functions are subspaces of V?
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(a) all f such that f(x2) = f(x)²;
(b) all f such that f(0) = f(1);
(c) all f such that f(3) = 1+ f(-5); d on
(d) all f such that f(-1) = 0;
(e) all f which are continuous.
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