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2021 LMT Spring
B10
2021 Spring LMT Division B Problem 10
2021 Spring LMT Division B Problem 10
Source:
January 22, 2022
algebra
Problem Statement
Let
f
(
x
)
f (x)
f
(
x
)
be a function mapping real numbers to real numbers. Given that
f
(
f
(
x
)
)
=
1
3
x
f (f (x)) =\frac{1}{3x}
f
(
f
(
x
))
=
3
x
1
, and
f
(
2
)
=
1
9
f (2) =\frac19
f
(
2
)
=
9
1
, find
f
(
1
6
)
f\left(\frac{1}{6}\right)
f
(
6
1
)
.Proposed by Zachary Perry
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