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Mathematics
Problem
Which of the following correctly describes the domain of the composite function
g
∘
f
g\circ f
g
∘
f
, where
f
:
A
→
B
f:A\to B
f
:
A
→
B
and
g
:
B
→
C
g:B\to C
g
:
B
→
C
? a)
dom
(
f
)
\operatorname{dom}(f)
dom
(
f
)
b)
{
x
∈
dom
(
f
)
∣
f
(
x
)
∈
dom
(
g
)
}
\{x\in\operatorname{dom}(f)\mid f(x)\in\operatorname{dom}(g)\}
{
x
∈
dom
(
f
)
∣
f
(
x
)
∈
dom
(
g
)}
c)
dom
(
f
)
∩
dom
(
g
)
\operatorname{dom}(f)\cap\operatorname{dom}(g)
dom
(
f
)
∩
dom
(
g
)
d)
{
x
∈
dom
(
f
)
∣
g
(
x
)
∈
dom
(
g
)
}
\{x\in\operatorname{dom}(f)\mid g(x)\in\operatorname{dom}(g)\}
{
x
∈
dom
(
f
)
∣
g
(
x
)
∈
dom
(
g
)}
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