If f(x) equal to (a) 1004 (c) 2007 4.t 4+2 2008 where x € Q, then Σ f(2009) is r=1 (b) 2006 (d) None

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.4: Definition Of Function
Problem 52E
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If f(x)
equal to
(a) 1004
(c) 2007
4*
4+2
2008
where x € Q, then (2009) is
Σ
r=1
(b) 2006
(d) None
Transcribed Image Text:If f(x) equal to (a) 1004 (c) 2007 4* 4+2 2008 where x € Q, then (2009) is Σ r=1 (b) 2006 (d) None
Let f(x) be a function satisfying the functional equation
f(x) + f(1 − x) = k, for every x € Q, where k is a constant
quantity.
Let m be a positive integer.
Π
Π
Π Π
Put x =
r
m + 1
1
\m + 1/ _ \ m+ 1
ΣπF)+Σ,+1=5)
m
r=l
m
in the given equation we get
r=1 m
Σ(+)+2+1)
m
22 141)
r=1
+
m
Σ AMF)
r=1
m + 1
m
where t = m + 1 - r.
= mk
m
mk
2
m
= mk
= mk
Transcribed Image Text:Let f(x) be a function satisfying the functional equation f(x) + f(1 − x) = k, for every x € Q, where k is a constant quantity. Let m be a positive integer. Π Π Π Π Put x = r m + 1 1 \m + 1/ _ \ m+ 1 ΣπF)+Σ,+1=5) m r=l m in the given equation we get r=1 m Σ(+)+2+1) m 22 141) r=1 + m Σ AMF) r=1 m + 1 m where t = m + 1 - r. = mk m mk 2 m = mk = mk
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