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Mathematics
Problem
Which of the following statements is always true for a bijective function
f
:
A
→
B
f:A\to B
f
:
A
→
B
with inverse
f
−
1
f^{-1}
f
−
1
? a)
f
∘
f
−
1
=
I
A
f\circ f^{-1}=I_A
f
∘
f
−
1
=
I
A
b)
f
−
1
(
a
)
=
1
f
(
a
)
for all
a
∈
A
f^{-1}(a)=\dfrac{1}{f(a)}\;\text{for all }a\in A
f
−
1
(
a
)
=
f
(
a
)
1
for all
a
∈
A
c)
f
−
1
∘
f
=
I
A
f^{-1}\circ f=I_A
f
−
1
∘
f
=
I
A
d)
f
−
1
∘
f
=
I
B
f^{-1}\circ f=I_B
f
−
1
∘
f
=
I
B
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