If-f-x-is-a-Continous-and-odd-function-Then-is-f-0-0-

Question Number 4873 by prakash jain last updated on 18/Mar/16

If f (x) is a Continous and odd function .

Then is f (0) = 0 ?

Commented by prakash jain last updated on 18/Mar/16

Thanks . That is what I thought but {couldn}^{'} t think of

proof .

Commented by Rasheed Soomro last updated on 19/Mar/16

f (0) = - f (0) \Rightarrow f (0) = 0 ?

H o w f (0) = 0 ?

Commented by 123456 last updated on 19/Mar/16

f (0) = - f (- 0) = - f (0)

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

2 f (0) = 0

f (0) = 0 / 2 = 0

Commented by Rasheed Soomro last updated on 19/Mar/16

T h α n k s!

Commented by 123456 last updated on 18/Mar/16

since f is continuous

\lim_{x \to 0} f (x) = f (0)

f (x) = - f (- x)

x = 0

f (0) = - f (0) \Rightarrow f (0) = 0

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