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Mathematics
Mathematics
Problem
For a real parameter
k
k
k
, let
f
k
(
x
)
=
{
x
2
−
k
,
0
≤
x
≤
2
k
ln
x
,
2
<
x
≤
4
f_k(x)= \begin{cases} x^{2}-k, & 0\le x\le 2\\[4pt] k\ln x, & 2< x\le 4 \end{cases}
f
k
(
x
)
=
{
x
2
−
k
,
k
ln
x
,
0
≤
x
≤
2
2
<
x
≤
4
Find all real values of
k
k
k
for which the equation
f
k
(
x
)
=
0
f_k(x)=0
f
k
(
x
)
=
0
has at least one solution in
[
0
,
4
]
[0,4]
[
0
,
4
]
.
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