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17
Math Prize 2013 Problem 17
Math Prize 2013 Problem 17
Source:
September 10, 2013
function
trigonometry
algebra
domain
Problem Statement
Let
f
f
f
be the function defined by
f
(
x
)
=
−
2
sin
(
π
x
)
f(x) = -2 \sin(\pi x)
f
(
x
)
=
−
2
sin
(
π
x
)
. How many values of
x
x
x
such that
−
2
≤
x
≤
2
-2 \le x \le 2
−
2
≤
x
≤
2
satisfy the equation
f
(
f
(
f
(
x
)
)
)
=
f
(
x
)
f(f(f(x))) = f(x)
f
(
f
(
f
(
x
)))
=
f
(
x
)
?
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