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1 If \( f ( x ) \) and \( g ( x ) \) be two given function with all real numbers as their domain, then \( h ( x ) = \langle f ( x ) + f ( - x ) ) ( g ( x ) - g ( - x ) ) \) . is (A) always an odd function (B) an odd function when both the \( f \) and \( g \) are odd (C) an odd function when \( f \) is even and \( g \) is odd (D) none of these

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Similar Questions

Q1

38. If f(x) and g(x) be two given function with all real numbers as their domain, then h(x) = {f(x)+f(-x)}{g(x)-g(-x)} is

1. Even

2. Odd

3. Even as well as odd

4. None

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Q2

Assertion :

f

is even,

g

is odd then

\frac{f}{g} (g \neq 0)

is an odd function. Reason: If

f (- x) = - f (x)

for every

x

of its domain then

f (x)

is called odd function and if

f (- x) = f (x)

for every

x

of its domain, then

f (x)

is called even function.

View Solution

Q3

If

f

is odd function ,

g

be an even function and

g (x) = f (x + 5)

then

f (x - 5)

equals

View Solution

Q4

If

f (x)

and

g (x)

be two given function with all real numbers as their domain

,

then

h (x) = f (x) + f (- x))

{g (x) - g (- x)}

is

View Solution

Q5

lf

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.

View Solution