If $f (x) + f (y) = f (x + y) f (x - y) \forall x, y$ , then $f (x)$ is
Even
Odd
Neither even nor odd
Both even, odd

Even

Neither even nor odd

Odd

Both even, odd

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f (x) + f (y) = f (x + y) f (x - y) \forall x, y

, then

f (x)

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If $$f:R-\left\{-1\right\} \to R$$ and $$f$$ is differentiable function satisfies:
$$f((x)+f(y)+xf(y))=y+f(x)+y f(x)\forall x, y\ \in R-\left\{-1\right\}$$. Find $$f(x)$$.

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f (x)

satisfies the relation

f (x + y) = f (x) + f (y)

for all

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and

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f (x)

is an odd function then-
(i)

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(ii)

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is even where [.] denotes greatest integer function.
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is neither even nor odd
(iv)

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Assertion :If

f (x + y) + f (x - y) = 2 f (x) f (y) \forall x, y \in R

and

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If f(x)+f(y)=f(x+y)f(x−y)∀ x, y, then f(x) isEvenOddNeither even nor oddBoth even, odd

If $f (x) + f (y) = f (x + y) f (x - y) \forall x, y$ , then $f (x)$ is
Even
Odd
Neither even nor odd
Both even, odd