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Serbia Team Selection Test
1987 Yugoslav Team Selection Test
Problem 2
composition of function involving sqrt(2+sqrt(2))
composition of function involving sqrt(2+sqrt(2))
Source: Yugoslav TST 1987 P2
May 28, 2021
function
algebra
Problem Statement
Let
f
(
x
)
=
2
+
2
x
+
2
−
2
−
2
−
2
x
+
2
+
2
f(x)=\frac{\sqrt{2+\sqrt2}x+\sqrt{2-\sqrt2}}{-\sqrt{2-\sqrt2}x+\sqrt{2+\sqrt2}}
f
(
x
)
=
−
2
−
2
x
+
2
+
2
2
+
2
x
+
2
−
2
. Find
f
(
f
(
⋯
f
⏟
1987
times
(
x
)
⋯
)
)
\underbrace{f(f(\cdots f}_{1987\text{ times}}(x)\cdots))
1987
times
f
(
f
(
⋯
f
(
x
)
⋯
))
.
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