math 3 10
x
1
0
1
0
1
0
1
x
1
0
1
0
1
0
1
f
f
(
-1
)
A
a
A
(
-1
)
a
f
f
(
-1
)
A
a
A
(
-1
)
a
x
x
x
x
1
λ
x
.
sin
(
x
+
1
)
x
↦
sin
(
x
+
1
)
x1
xn
expression-in-x1-xn
lambda
x1
xn
expression-in-x1-xn
x1
xn
D
expression-in-x1-xn
restriction
lambda
x1
xn
expression-in-x1-xn
D
f
g
h
f
∘
g
∘
h
f
g
x
f
g
x
(
f
∘
g
)
x
=
f
g
x
f
f
f
∘
f
(
-1
)
=
id
f
domain
f
=
R
f
codomain
f
=
Q
-1
1
image
sin
=
-1
1
x
x
0
0
x
0
x
x
0
{
−
x
if
x
<
0
0
if
x
=
0
x
if
x
>
0
0
x
0
1
x
1
x
piecewise
piece
0
lt
x
0
piece
1
gt
x
1
otherwise
x
a
b
⌊
a
/
b
⌋
n
n
!
a
b
a
/
b
2
3
5
max
{
2
,
3
,
5
}
y
y
0
1
y
3
max
{
y
|
y
3
∈
0
1
}
a
b
min
{
a
,
b
}
x
x
B
x
2
min
{
x
2
|
x
∉
B
}
3
−
3
x
y
x
−
y
x
y
z
x
+
y
+
z
x
3
x
3
a
b
a
mod
b
a
b
a
b
n
a
a
n
x
root
x
2
n
a
root
a
n