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Problem
Problem
Let
f
(
x
)
=
a
x
+
b
f(x) = ax + b
f
(
x
)
=
a
x
+
b
and
g
(
x
)
=
c
x
+
d
g(x) = cx + d
g
(
x
)
=
c
x
+
d
,
a
≠
0
a \neq 0
a
=
0
,
c
≠
0
c \neq 0
c
=
0
. Assume
a
=
1
a = 1
a
=
1
,
b
=
2
b = 2
b
=
2
. If
(
f
∘
g
)
(
x
)
=
(
g
∘
f
)
(
x
)
(f \circ g)(x) = (g \circ f)(x)
(
f
∘
g
)
(
x
)
=
(
g
∘
f
)
(
x
)
for all
x
x
x
, what can you say about
c
c
c
and
d
d
d
(a)
c
c
c
and
d
d
d
both arbitrary (b)
c
=
1
c = 1
c
=
1
,
d
d
d
arbitrary (c)
c
c
c
arbitrary,
d
=
1
d = 1
d
=
1
(d)
c
=
1
c = 1
c
=
1
,
d
=
1
d = 1
d
=
1
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