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Mathematics
Mathematics
Problem
For
k
∈
R
k\in\mathbb R
k
∈
R
, define
f
k
:
R
→
R
f_k:\mathbb R\rightarrow\mathbb R
f
k
:
R
→
R
by
f
k
(
x
)
=
k
x
2
+
(
k
−
2
)
x
+
1
f_k(x)=kx^{2}+(k-2)x+1
f
k
(
x
)
=
k
x
2
+
(
k
−
2
)
x
+
1
. For which value(s) of
k
k
k
is
f
k
f_k
f
k
injective on
R
\mathbb R
R
? a) All
k
>
0
k>0
k
>
0
b) Only
k
=
0
k=0
k
=
0
c)
4
−
2
3
<
k
<
4
+
2
3
4-2\sqrt{3}<k<4+2\sqrt{3}
4
−
2
3
<
k
<
4
+
2
3
d) Only
k
=
2
k=2
k
=
2
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