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Mathematics
Mathematics
Problem
Consider the sets
A
=
{
1
,
2
,
3
}
A=\{1,2,3\}
A
=
{
1
,
2
,
3
}
and
B
=
{
4
,
5
,
6
}
B=\{4,5,6\}
B
=
{
4
,
5
,
6
}
. A bijection
f
:
A
→
B
f:A\to B
f
:
A
→
B
is given by
f
(
1
)
=
5
,
f
(
2
)
=
4
,
f
(
3
)
=
6
f(1)=5,\ f(2)=4,\ f(3)=6
f
(
1
)
=
5
,
f
(
2
)
=
4
,
f
(
3
)
=
6
. Let
f
−
1
f^{-1}
f
−
1
be the inverse of
f
f
f
. Evaluate
(
f
−
1
∘
f
)
(
2
)
(f^{-1}\circ f)(2)
(
f
−
1
∘
f
)
(
2
)
. a)
5
5
5
b) Undefined c)
2
2
2
d)
4
4
4
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