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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
x
f(x)=\sqrt{x}
f
(
x
)
=
x
and
g
(
x
)
=
1
2
x
+
k
g(x)=\tfrac{1}{2}x+k
g
(
x
)
=
2
1
x
+
k
defined on the closed interval
[
0
,
1
]
[0,1]
[
0
,
1
]
, where
k
k
k
is a real constant. Determine all real values of
k
k
k
for which the equation
f
(
x
)
=
g
(
x
)
f(x)=g(x)
f
(
x
)
=
g
(
x
)
has at least one solution in
[
0
,
1
]
[0,1]
[
0
,
1
]
.
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