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Mathematics
Problem
For an invertible function
f
:
A
→
B
f:A\to B
f
:
A
→
B
with inverse
f
−
1
f^{-1}
f
−
1
, which of the following identities is ALWAYS true for every
x
∈
A
x\in A
x
∈
A
? a)
f
(
f
−
1
(
x
)
)
=
x
f\bigl(f^{-1}(x)\bigr)=x
f
(
f
−
1
(
x
)
)
=
x
b)
f
(
f
(
x
)
)
=
x
f\bigl(f(x)\bigr)=x
f
(
f
(
x
)
)
=
x
c)
f
−
1
(
f
(
x
)
)
=
x
f^{-1}\bigl(f(x)\bigr)=x
f
−
1
(
f
(
x
)
)
=
x
d)
f
−
1
(
x
)
=
f
(
x
)
f^{-1}(x)=f(x)
f
−
1
(
x
)
=
f
(
x
)
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