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Question

Iff:RR be a function satisfying the functional Rule f(x+f(y))=f(x)+x+f(xy);x,yR then
Column IColumn II(P)f(0)(A)1(Q)|f(1)+f(2)|(B)3(R)|f(2)+f(3)|(C)0(S)|f(1)+f(3)|(D)2
  1. PB,QA,RC,SD
  2. PA,QB,RD,SC
  3. PC,QB,RA,SD
  4. PC,QB,RD,SA


Solution

The correct option is C PC,QB,RA,SD
Put y = 0 in the given equation and let f(0) = k
f(x+k) = 2f(x)+x
Put x =-k, k =2 f(-k) -k
f(-k) = k
Put y = -k in functional definition, then
f(x+k) =f(x) + x+ f(x+k)
f(x) =-x

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