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Question


Given that a real value function g, is such that g(a+b)=a+g(g(b)) & g(0)=0. Find g(102)?


Options:
A .   0
B .   1
C .   99
D .   102
Answer: Option D
:
D

Assumption


Assume a=0, b=0


g(0)=0+g(g(0))=0


Next assume a=1 and b=0


g(1)=1+g(g(0))=1+0=1


continue in the same way, assume a=2, b=0


g(2)=2+g(g(0))=2


Hence g(x)= x itself. Hence g(102)=102



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