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Mathematics
Problem
Let
f
(
x
)
=
k
x
+
1
f(x)=kx+1
f
(
x
)
=
k
x
+
1
and
g
(
x
)
=
x
+
2
g(x)=x+2
g
(
x
)
=
x
+
2
. For which value of
k
k
k
does
(
f
∘
g
)
(
x
)
=
(
g
∘
f
)
(
x
)
(f\circ g)(x)=(g\circ f)(x)
(
f
∘
g
)
(
x
)
=
(
g
∘
f
)
(
x
)
hold for all real
x
x
x
? a)
k
=
1
2
k=\dfrac12
k
=
2
1
b)
k
=
1
k=1
k
=
1
c)
k
=
2
k=2
k
=
2
d) Any\;\text{real}\;k$
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