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Problem
Problem
Let
f
:
[
0
,
∞
)
→
[
0
,
∞
)
f:[0,\infty)\rightarrow[0,\infty)
f
:
[
0
,
∞
)
→
[
0
,
∞
)
be a function defined by
f
(
x
)
=
x
2
+
(
k
2
−
3
k
+
2
)
x
+
k
2
−
k
f(x)=x^2+(k^2-3k+2)x+k^2-k
f
(
x
)
=
x
2
+
(
k
2
−
3
k
+
2
)
x
+
k
2
−
k
. If
f
(
x
)
f(x)
f
(
x
)
is both injective and surjective, then the number of integers in the range of
k
k
k
is
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