Question
If f(x)+2f(1−x)=x2+1 ∀ xϵR then f(x) is
Answer: Option C
:
C
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C
f(x)+2f(1−x)=x2+1 .........(i)
Replacing x by 1 – x
f(1−x)+2f(x)=(1−x2)+1 .......(ii)
multiplying (ii) by 2 and subtracting it from (1), we get
−3f(x)=x2−2(1−x)2−1
3f(x)=2(1−x)2+1−x2=(1−x)(2−2x+1+x)=(1−x)(3−x)=x2−4x+3
f(x)=13(x2−4x+3)
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