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Mathematics
Problem
Let
h
(
x
)
=
sin
(
(
x
2
−
1
)
3
)
h(x)=\sin\bigl((x^{2}-1)^{3}\bigr)
h
(
x
)
=
sin
(
(
x
2
−
1
)
3
)
. Which ordered triple
(
r
,
q
,
p
)
(r,\,q,\,p)
(
r
,
q
,
p
)
of functions satisfies
h
=
p
∘
q
∘
r
h = p\circ q\circ r
h
=
p
∘
q
∘
r
where
(
p
∘
q
∘
r
)
(
x
)
=
p
(
q
(
r
(
x
)
)
)
(p\circ q\circ r)(x)=p\bigl(q(r(x))\bigr)
(
p
∘
q
∘
r
)
(
x
)
=
p
(
q
(
r
(
x
))
)
? a)
r
(
x
)
=
x
3
,
q
(
u
)
=
u
2
−
1
,
p
(
v
)
=
sin
v
r(x)=x^{3},\; q(u)=u^{2}-1,\; p(v)=\sin v
r
(
x
)
=
x
3
,
q
(
u
)
=
u
2
−
1
,
p
(
v
)
=
sin
v
b)
r
(
x
)
=
x
2
−
1
,
q
(
u
)
=
u
3
,
p
(
v
)
=
sin
v
r(x)=x^{2}-1,\; q(u)=u^{3},\; p(v)=\sin v
r
(
x
)
=
x
2
−
1
,
q
(
u
)
=
u
3
,
p
(
v
)
=
sin
v
c)
r
(
x
)
=
x
2
−
1
,
q
(
u
)
=
sin
u
,
p
(
v
)
=
v
3
r(x)=x^{2}-1,\; q(u)=\sin u,\; p(v)=v^{3}
r
(
x
)
=
x
2
−
1
,
q
(
u
)
=
sin
u
,
p
(
v
)
=
v
3
d)
r
(
x
)
=
sin
x
,
q
(
u
)
=
u
3
,
p
(
v
)
=
v
2
−
1
r(x)=\sin x,\; q(u)=u^{3},\; p(v)=v^{2}-1
r
(
x
)
=
sin
x
,
q
(
u
)
=
u
3
,
p
(
v
)
=
v
2
−
1
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