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Mathematics
Problem
Let
f
:
A
→
B
f:A\to B
f
:
A
→
B
and
g
:
B
→
C
g:B\to C
g
:
B
→
C
be bijections. For every
c
∈
C
c\in C
c
∈
C
, which of the following is always equal to
(
g
∘
f
)
−
1
(
c
)
(g\circ f)^{-1}(c)
(
g
∘
f
)
−
1
(
c
)
? a)
g
−
1
(
f
−
1
(
c
)
)
g^{-1}\bigl(f^{-1}(c)\bigr)
g
−
1
(
f
−
1
(
c
)
)
b)
g
−
1
(
f
(
c
)
)
g^{-1}\bigl(f(c)\bigr)
g
−
1
(
f
(
c
)
)
c)
f
−
1
(
g
−
1
(
c
)
)
f^{-1}\bigl(g^{-1}(c)\bigr)
f
−
1
(
g
−
1
(
c
)
)
d)
f
(
g
−
1
(
c
)
)
f\bigl(g^{-1}(c)\bigr)
f
(
g
−
1
(
c
)
)
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