16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 2.2.2

Vector Spaces

Mathematics — Linear Algebra · subspaces-of-function-spaces

Problem

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^2) = 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.