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Problems
Let
f
:
[
−
2
+
1
,
2
+
1
]
→
[
−
2
+
1
2
,
2
+
1
2
]
f:[-\sqrt{2}+1,\sqrt{2}+1]\rightarrow\left[-\frac{\sqrt{2}+1}{2},\frac{\sqrt{2}+1}{2}\right]
f
:
[
−
2
+
1
,
2
+
1
]
→
[
−
2
2
+
1
,
2
2
+
1
]
…
Problem
Let
f
:
[
−
2
+
1
,
2
+
1
]
→
[
−
2
+
1
2
,
2
+
1
2
]
f:[-\sqrt{2}+1,\sqrt{2}+1]\rightarrow\left[-\frac{\sqrt{2}+1}{2},\frac{\sqrt{2}+1}{2}\right]
f
:
[
−
2
+
1
,
2
+
1
]
→
[
−
2
2
+
1
,
2
2
+
1
]
be a function defined by
f
(
x
)
=
1
−
x
1
+
x
2
f(x)=\frac{1-x}{1+x^2}
f
(
x
)
=
1
+
x
2
1
−
x
. If
f
−
1
(
x
)
=
{
−
1
+
λ
(
4
x
−
4
x
2
+
1
)
2
x
,
x
≠
0
,
μ
,
x
=
0
f^{-1}(x)=\begin{cases}\frac{-1+\lambda(\sqrt{4x-4x^2+1})}{2x}, & x\neq 0,\\ \mu, & x=0\end{cases}
f
−
1
(
x
)
=
{
2
x
−
1
+
λ
(
4
x
−
4
x
2
+
1
)
,
μ
,
x
=
0
,
x
=
0
, then
λ
+
μ
\lambda+\mu
λ
+
μ
is:
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