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Mathematics
Problem
Determine all real numbers
a
a
a
such that the function
f
:
R
∖
{
−
a
}
→
R
∖
{
1
}
f:\mathbb R\setminus\{-a\}\to \mathbb R\setminus\{1\}
f
:
R
∖
{
−
a
}
→
R
∖
{
1
}
defined by
f
(
x
)
=
x
x
+
a
f(x)=\dfrac{x}{x+a}
f
(
x
)
=
x
+
a
x
is invertible.
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