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Mathematics
Mathematics
Problem
Which of the following properties is sufficient to conclude that a function
h
h
h
is odd? a)
h
(
−
x
)
=
h
(
x
)
h(-x)=h(x)
h
(
−
x
)
=
h
(
x
)
\text{ for every real number }x b)
∫
−
a
a
h
(
x
)
d
x
=
0
for all
a
>
0
\displaystyle \int_{-a}^{a} h(x)\,dx =0\text{ for all }a>0
∫
−
a
a
h
(
x
)
d
x
=
0
for all
a
>
0
c)
h
(
−
x
)
=
−
h
(
x
)
h(-x)=-h(x)
h
(
−
x
)
=
−
h
(
x
)
\text{ for every real number }x d)
h
(
x
)
=
−
h
(
−
x
)
h(x)=-h(-x)
h
(
x
)
=
−
h
(
−
x
)
\text{ only when }x>0$
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