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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
x
−
x
2
f(x) = x - x^2
f
(
x
)
=
x
−
x
2
and
g
(
x
)
=
{
x
}
g(x) = \{x\}
g
(
x
)
=
{
x
}
,
∀
x
∈
R
\forall x \in R
∀
x
∈
R
where
{
}
\{ \}
{
}
denotes fractional part function. a. Statement I
f
(
g
(
x
)
)
f(g(x))
f
(
g
(
x
))
will be continuous,
∀
x
∈
R
\forall x \in R
∀
x
∈
R
. b. Statement II
f
(
0
)
=
f
(
1
)
f(0) = f(1)
f
(
0
)
=
f
(
1
)
and
g
(
x
)
g(x)
g
(
x
)
is periodic with period 1.
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