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Mathematics
Problem
54. Is Function Composition Associative? You already know that function composition is not commutative; that is,
(
f
∘
g
)
(
x
)
≠
(
g
∘
f
)
(
x
)
(f \circ g)(x) \neq(g \circ f)(x)
(
f
∘
g
)
(
x
)
=
(
g
∘
f
)
(
x
)
. But is function composition associative? That is, does
(
f
∘
(
g
∘
h
)
)
(
x
)
=
(
(
f
∘
g
)
∘
h
)
)
(
x
)
(f \circ(g \circ h))(x)=((f \circ g) \circ h)) (x)
(
f
∘
(
g
∘
h
))
(
x
)
=
((
f
∘
g
)
∘
h
))
(
x
)
? Explain your answer.
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