# If f(x)+f(y)=f(x+y) prove that is an odd function

2
by namku

2015-05-04T12:15:05+05:30

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put :

put

which is exactly the definition of an odd function
2015-05-04T12:24:48+05:30

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F (x) + f (y) = f (x + y)    for all real values of x and y.

let x = 0, and y = 0.
f(0) + f(0) = f (0+0) = f (0)
=> f (0) = 0      ---- (1)

let x = - y  then

f ( x ) + f (- x)   = f ( x - x ) = f (0) = 0

=> f (-x) = - f ( x)      ,  as their sum is 0.          --- (2)

=>  function f  is an odd function, as    (1) and (2)

that is image wrt y axis is minus of its value, for an odd function.

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