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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
a
x
−
1
x
+
a
f(x)=\dfrac{a x-1}{x+a}
f
(
x
)
=
x
+
a
a
x
−
1
, where
a
≠
−
1
a\neq -1
a
=
−
1
and
x
≠
−
a
x\neq -a
x
=
−
a
. Determine all real values of
a
a
a
for which
f
f
f
equals its own inverse.
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