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1. f(x)+f(x-1/x)=x+1,find f(x),x nt equal to 1,0 2. 2f(x)+f(1-x/x)=x,x nt equal to 0

1. f(x)+f(x-1/x)=x+1,find f(x),x nt equal to 1,0
2. 2f(x)+f(1-x/x)=x,x nt equal to 0

Grade:12

1 Answers

Kapil Upadhyay
29 Points
8 years ago

  f(x)+ f(x-1/x)=1+x       -----1

 Replace x by (x-1/x)

f(x-1/x) +f(-1/x-1)=1+ x-1/x      -------2

by 1 & 2

f(x) -f(-1/x-1)=x - (x-1/x)           ----------3

replace x by (-1/x-1)

f(-1/x-1) -f(x-1/x)=-1/x-1 -x

f(-1/x-1) + f(x)=1 -1/x-1       -----------4

add 3 & 4

f(x)=(x3-x2-1)/2x(x-1)

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