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Mathematics
Mathematics
Problem
Explain why the domain of the composite function
(
g
∘
f
)
(g \circ f)
(
g
∘
f
)
equals
{
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
)}
when
f
:
A
→
B
f:A \to B
f
:
A
→
B
and
g
:
B
→
C
g:B \to C
g
:
B
→
C
are real-valued functions.
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