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question is …....f(x+y)=f(x)+f(y) is a odd function prove..... i added image of solution of this question .please help me to understand solution …..i cant understand the solution which give in my book...........

question is …....f(x+y)=f(x)+f(y) is a odd function prove.....
i added image of  solution of this question .please help me to understand solution …..i cant understand the solution which give in my book...........

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Grade:12

1 Answers

Shobhit Varshney IIT Roorkee
askIITians Faculty 33 Points
9 years ago
HI,

Don’t follow this solution, it makes no sense to me.
See, f(x+y) = f(x) + f(y)

Put y = 0, f(x+0) = f(x) + f(0)
So, f(0) = 0

Now, put y = -x, f(x-x) = f(x) + f(-x)
So, f(0) = f(x) + f(-x)
So, 0 = f(x) + f(-x)
So, f(-x) = -f(x)

therefore, f(x) is an odd function.

thanks

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