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f-x-3-x-1-f-x-3-1-x-x-find-f-x-

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Question Number 87755 by john santu last updated on 06/Apr/20
f(((x−3)/(x+1))) + f(((x+3)/(1−x))) = x find f(x)
f(x−3x+1)+f(x+31−x)=xfindf(x)
Commented by john santu last updated on 06/Apr/20
(i) let ((x−3)/(x+1)) = x′ ⇒f(x′) + f(((x′−3)/(x′+1))) = ((x′+3)/(1−x)) (ii) let ((x+3)/(1−x)) = x′⇒ f(((x′+3)/(1−x′))) +f(x′) = ((x′−3)/(x′+1)) eq +(i)+(ii) 2 [ f(((x−3)/(x+1)))+f(((x+3)/(1−x)))+f(x) ] = x+((x+3)/(1−x))+((x−3)/(x+1)) 2 [ x +f(x) ] = ((x(1−x^2 )+x^2 +4x+3−x^2 +4x−3)/(1−x^2 )) 2 [ x+f(x) ] = ((−x^3 +9x)/(1−x^2 )) f(x) = ((9x−x^3 )/(2−2x^2 )) − ((x(2−2x^2 ))/(2−2x^2 )) f(x) = ((x^3 +7x)/(2−2x^2 )) .
(i)letx−3x+1=x′⇒f(x′)+f(x′−3x′+1)=x′+31−x(ii)letx+31−x=x′⇒f(x′+31−x′)+f(x′)=x′−3x′+1eq+(i)+(ii)2[f(x−3x+1)+f(x+31−x)+f(x)]=x+x+31−x+x−3x+12[x+f(x)]=x(1−x2)+x2+4x+3−x2+4x−31−x22[x+f(x)]=−x3+9x1−x2f(x)=9x−x32−2x2−x(2−2x2)2−2x2f(x)=x3+7x2−2x2.
Commented by jagoll last updated on 06/Apr/20
thank you mister. ilike this question
thankyoumister.ilikethisquestion

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