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Question

If f(x+f(y))=f(x)+y x,yR and f(0)=1, then the value of f(7) is

A
1
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B
7
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C
6
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D
8
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Solution

The correct option is A 1
f(x+f(y))=f(x)+y, f(0)=1
Putting y=0, we get
f(x+f(0))=f(x)+0
or, f(x+1)=f(x) xR
Thus, f(x) is periodic with 1 as one of its period. Hence,
f(7)=f(6)=f(5)==f(1)=f(0)=1

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