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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 (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); ds oob sd iliw eidT a0aqe oldetire e bul deum ow laoin VIPoney me mens %3D

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 (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); ds oob sd iliw eidT a0aqe oldetire e bul deum ow laoin VIPoney me mens %3D

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? of won D (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) all f such that f(-1) = 0; (e) all f which are continuous. SUBD ew dguonIAsoAga a bnt dem ow Jasin snob .9oaqe nodoov %3D gla oldetive laois %D ed liw eidT %3D ood V ioisinited
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? of won D (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) all f such that f(-1) = 0; (e) all f which are continuous. SUBD ew dguonIAsoAga a bnt dem ow Jasin snob .9oaqe nodoov %3D gla oldetive laois %D ed liw eidT %3D ood V ioisinited
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