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National High School Mathematics League
1984 National High School Mathematics League
6
Some Equalities about Function
Some Equalities about Function
Source: 1984 National High School Mathematics League, Exam One, Problem 6
February 22, 2020
function
Problem Statement
If
F
(
1
−
x
1
+
x
)
=
x
F(\frac{1-x}{1+x})=x
F
(
1
+
x
1
−
x
)
=
x
, then
(A)
F
(
−
2
−
x
)
=
−
2
−
F
(
x
)
(B)
F
(
−
x
)
=
F
(
1
+
x
1
−
x
)
\text{(A)}F(-2-x)=-2-F(x)\qquad\text{(B)}F(-x)=F(\frac{1+x}{1-x})
(A)
F
(
−
2
−
x
)
=
−
2
−
F
(
x
)
(B)
F
(
−
x
)
=
F
(
1
−
x
1
+
x
)
(C)
F
(
1
x
)
=
F
(
x
)
(D)
F
(
F
(
−
x
)
)
=
−
x
\text{(C)}F(\frac{1}{x})=F(x)\qquad\text{(D)}F(F(-x))=-x
(C)
F
(
x
1
)
=
F
(
x
)
(D)
F
(
F
(
−
x
))
=
−
x
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