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Problem
Problem
If
f
:
[
1
,
∞
)
→
R
f: [1, \infty) \to R
f
:
[
1
,
∞
)
→
R
:
f
(
x
)
f(x)
f
(
x
)
is monotonic and differentiable function and
f
(
1
)
=
1
f(1) = 1
f
(
1
)
=
1
, then number of solutions of the equation
f
(
f
(
x
)
)
=
1
x
2
−
2
x
+
2
f(f(x)) = \frac{1}{x^2 - 2x + 2}
f
(
f
(
x
))
=
x
2
−
2
x
+
2
1
is/are ....
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