Can f(0)=0 be always an odd function?

Let f(x) be a real function with domain R. We can check whether it is an odd function simply by putting x=0 in f(x).If f(0)=0 then it is an odd function. Is it always true for all the cases? Can we fully rely on it for checking whether the function is odd or not?

#Calculus

Easy Math Editor

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Comments

What about $f(x) = \ln(1 + x^2)$ or $f(x) = x^2$ ?

These are real functions with domain $\mathbb R$ and also satisfy the condition $f(0) = 0$ even though they aren't odd functions. Instead, these are even functions.

Arkajyoti Banerjee - 3 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$