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Mathematics
Mathematics
Problem
Consider the function
f
(
x
)
=
x
+
a
x
−
1
f(x) = \frac{x+a}{x-1}
f
(
x
)
=
x
−
1
x
+
a
,
x
∈
R
−
{
1
}
x \in \mathbb{R} - \{1\}
x
∈
R
−
{
1
}
where
a
a
a
is a real constant. If
f
f
f
is not a constant function then find the value of
f
(
1
f
(
f
(
x
)
)
)
−
f
(
f
(
f
(
1
x
)
)
)
f\left(\frac{1}{f(f(x))}\right) - f\left(f\left(f\left(\frac{1}{x}\right)\right)\right)
f
(
f
(
f
(
x
))
1
)
−
f
(
f
(
f
(
x
1
)
)
)
.
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