Question

# Iff:R→R be a function satisfying the functional Rule f(x+f(y))=f(x)+x+f(x−y);∀x,y∈R 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)2P→B,Q→A,R→C,S→DP→A,Q→B,R→D,S→CP→C,Q→B,R→A,S→DP→C,Q→B,R→D,S→A

Solution

## The correct option is C P→C,Q→B,R→A,S→DPut 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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