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Mathematics
Problem
Let
f
(
x
)
=
x
2
+
1
f(x)=x^{2}+1
f
(
x
)
=
x
2
+
1
for
x
∈
[
1
,
4
]
x\in[1,4]
x
∈
[
1
,
4
]
and let
g
k
(
x
)
=
k
x
g_k(x)=k x
g
k
(
x
)
=
k
x
, where
k
k
k
is a real parameter. For which values of
k
k
k
is there at least one number
c
c
c
in
[
1
,
4
]
[1,4]
[
1
,
4
]
such that
f
(
c
)
=
g
k
(
c
)
f(c)=g_k(c)
f
(
c
)
=
g
k
(
c
)
? a)
k
≥
2
k\ge 2
k
≥
2
b)
k
∈
(
2
,
17
4
)
k\in(2,\,\dfrac{17}{4})
k
∈
(
2
,
4
17
)
c)
k
∈
[
2
,
17
4
]
k\in[2,\,\dfrac{17}{4}]
k
∈
[
2
,
4
17
]
d)
k
∈
[
2
,
4
]
k\in[2,\,4]
k
∈
[
2
,
4
]
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