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Mathematics
Mathematics
Problem
For
k
∈
R
k\in\mathbb R
k
∈
R
, define
f
(
x
)
=
x
+
2
f(x)=x+2
f
(
x
)
=
x
+
2
and
g
(
x
)
=
k
x
g(x)=kx
g
(
x
)
=
k
x
on
R
\mathbb R
R
. Determine all real values of
k
k
k
for which
f
∘
g
=
g
∘
f
f\circ g=g\circ f
f
∘
g
=
g
∘
f
as functions on
R
\mathbb R
R
.
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