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Mathematics
Mathematics
Problem
Define
f
:
R
∖
{
−
1
}
→
R
∖
{
p
}
f:\mathbb{R}\setminus\{-1\}\to\mathbb{R}\setminus\{p\}
f
:
R
∖
{
−
1
}
→
R
∖
{
p
}
by
f
(
x
)
=
p
x
+
2
x
+
1
f(x)=\dfrac{px+2}{x+1}
f
(
x
)
=
x
+
1
p
x
+
2
, where
p
p
p
is a real parameter. The function
f
f
f
is bijective precisely when a)
p
=
2
p=2
p
=
2
b)
p
≠
2
p\ne 2
p
=
2
c)
p
=
1
p=1
p
=
1
d)
p
≠
1
2
p\ne\dfrac12
p
=
2
1
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