"If \\( f ( x ) + f ( v ) = f ( x + y ) f ( x - y ) \\forall x , y , \\) then \\( f ( x ) \\) is\na) even\nc) Neither even nor odd"

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Similar Questions

f (x)

is an odd function then-
(i)

\frac{f (- x) + f (x)}{2}

is an even function
(ii)

[∣ f (x) ∣ + 1]

is even where [.] denotes greatest integer function.
(iii)

\frac{f (x) - f (- x)}{2}

is neither even nor odd
(iv)

f (x) + f (- x)

is neither even nor odd
Which of these statements are correct

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If f(x) =

x^{2}

and g(x) =

l o g_{e}

x, then f(x) + g(x) will be

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

, then

f (x)

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Assertion :Let

f (x) = {\begin{matrix} x, & x \in Q 1 - x, & x \notin Q \end{matrix}

, then

f (f (x)) = x

. Reason:

f (x)

is neither odd nor even.

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f (x)

and

g (x)

are two functions such that

f (x) + g (x) = e^{x}

and

f (x) - g (x) = e^{- x}

then
I:

f (x)

is an even function
II:

g (x)

is an odd function
III: Both

f (x)

and

g (x)

are neither even nor odd.

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