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 . &nbsp0 B . &nbsp1 C . &nbsp99 D . &nbsp102

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

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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