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Mathematics
Mathematics
Problem
Let
a
a
a
be a real parameter. Determine all values of
a
a
a
for which the function
f
a
(
x
)
=
arcsin
(
a
x
)
f_a(x)=\arcsin(ax)
f
a
(
x
)
=
arcsin
(
a
x
)
is defined and satisfies
f
a
(
x
)
≤
0
f_a(x)\le 0
f
a
(
x
)
≤
0
for every
x
∈
[
0
,
1
2
]
x \in \left[0,\dfrac{1}{2}\right]
x
∈
[
0
,
2
1
]
.
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