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If satisfies
MATHEMATICS · Single correct · AoPS · Mathematics · Functions · Functions
Problem
If
f
:
(
0
,
∞
)
→
(
0
,
∞
)
f:(0,\infty)\to(0,\infty)
f
:
(
0
,
∞
)
→
(
0
,
∞
)
satisfies
f
(
x
f
(
y
)
)
=
x
2
y
a
f(xf(y))=x^2y^a
f
(
x
f
(
y
))
=
x
2
y
a
, where
a
∈
R
a\in\mathbb{R}
a
∈
R
, then the value of
a
a
a
is (a)
4
4
4
(b)
2
2
2
(c)
2
\sqrt{2}
2
(d)
1
1
1
Related theory
Functions
Composition of Functions
Exponential and Logarithmic Functions
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