Determine whether the following are subspaces of C [ − 1 , 1 ] : (a) The set of functionsf in C [ − 1 , 1 ] such that f ( − 1 ) = f ( 1 ) (b) The set of odd functions in C [ − 1 , 1 ] (c) The set of continuous nondecreasing functionson [ − 1 , 1 ] (d) The set of functionsf in C [ − 1 , 1 ] such that f ( − 1 ) = 0 and f ( 1 ) = 0 (e) The set of functions f in C [ − 1 , 1 ] such that f ( − 1 ) = 0 and f ( 1 ) = 0
Determine whether the following are subspaces of C [ − 1 , 1 ] : (a) The set of functionsf in C [ − 1 , 1 ] such that f ( − 1 ) = f ( 1 ) (b) The set of odd functions in C [ − 1 , 1 ] (c) The set of continuous nondecreasing functionson [ − 1 , 1 ] (d) The set of functionsf in C [ − 1 , 1 ] such that f ( − 1 ) = 0 and f ( 1 ) = 0 (e) The set of functions f in C [ − 1 , 1 ] such that f ( − 1 ) = 0 and f ( 1 ) = 0
Determine whether the following are subspaces of
C
[
−
1
,
1
]
: (a) The set of functionsf in
C
[
−
1
,
1
]
such that
f
(
−
1
)
=
f
(
1
)
(b) The set of odd functions in
C
[
−
1
,
1
]
(c) The set of continuous nondecreasing functionson
[
−
1
,
1
]
(d) The set of functionsf in
C
[
−
1
,
1
]
such that
f
(
−
1
)
=
0
and
f
(
1
)
=
0
(e) The set of functions f in
C
[
−
1
,
1
]
such that
f
(
−
1
)
=
0
and
f
(
1
)
=
0
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