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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? Won T VIonty me ransA laois (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)3; (d) all f such that f(-1)%3D0: %3D oldedive ohob ed lliw aidT anaqe bail sem ow

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? Won T VIonty me ransA laois (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)3; (d) all f such that f(-1)%3D0: %3D oldedive ohob ed lliw aidT anaqe bail sem ow

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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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? (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. VIPonep me mans eldetive a bnt sem ow aon onob ed liw aidT aoaqe todoov %3D ad V i oitiai d
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? (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. VIPonep me mans eldetive a bnt sem ow aon onob ed liw aidT aoaqe todoov %3D ad V i oitiai d
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