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Mathematics
Mathematics
Problem
Let
f
:
R
∖
{
−
1
}
→
R
f:\mathbb R\setminus\{-1\}\to\mathbb R
f
:
R
∖
{
−
1
}
→
R
be defined by
f
(
x
)
=
a
x
+
1
x
+
1
f(x)=\dfrac{ax+1}{x+1}
f
(
x
)
=
x
+
1
a
x
+
1
, where
a
∈
R
a\in\mathbb R
a
∈
R
. Determine all real values of
a
a
a
for which
f
f
f
is injective on its domain.
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