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Mathematics
Problem
Consider
f
(
x
)
=
2
x
+
1
x
−
3
f(x)=\dfrac{2x+1}{x-3}
f
(
x
)
=
x
−
3
2
x
+
1
,
x
≠
3
x\neq 3
x
=
3
, and
g
(
x
)
=
3
x
+
p
x
−
2
g(x)=\dfrac{3x+p}{x-2}
g
(
x
)
=
x
−
2
3
x
+
p
defined on their natural domains. For which value of
p
p
p
does the composition
g
∘
f
g\circ f
g
∘
f
equal the identity function on the domain of
f
f
f
? a)
2
2
2
b)
1
1
1
c)
3
3
3
d)
−
5
-5
−
5
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