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2017 Junior Regional Olympiad - FBH
1
Junior Regional Olympiad - FBH 2017 Grade 8 Problem 1
Junior Regional Olympiad - FBH 2017 Grade 8 Problem 1
Source:
September 20, 2018
algebra
functions
function
functional equation
Problem Statement
It is given function
f
(
x
)
=
3
x
−
2
f(x)=3x-2
f
(
x
)
=
3
x
−
2
a
)
a)
a
)
Find
g
(
x
)
g(x)
g
(
x
)
if
f
(
2
x
−
g
(
x
)
)
=
−
3
(
1
+
2
m
)
x
+
34
f(2x-g(x))=-3(1+2m)x+34
f
(
2
x
−
g
(
x
))
=
−
3
(
1
+
2
m
)
x
+
34
b
)
b)
b
)
Solve the equation:
g
(
x
)
=
4
(
m
−
1
)
x
−
4
(
m
+
1
)
g(x)=4(m-1)x-4(m+1)
g
(
x
)
=
4
(
m
−
1
)
x
−
4
(
m
+
1
)
,
m
∈
R
m \in \mathbb{R}
m
∈
R
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