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put :

put :

which is exactly the definition of an odd function

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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)

=>

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

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.