y-x-f-x-g-x-h-x-y-x-x-2-sin-x-x-1-x-f-x-is-even-g-x-is-odd-f-0-g-0-h-0-

Question Number 4844 by 123456 last updated on 17/Mar/16

y (x) = f (x) + g (x) + h (x)

y (x) = x^{2} + \sin x + x (1 - x)

f (x) is even

g (x) is odd

f (0) g (0) - h (0) = ?

Commented by Rasheed Soomro last updated on 17/Mar/16

y (x) = f (x) + g (x) + h (x)

y (x) = x^{2} + \sin x + x (1 - x) \Rightarrow y (0) = 0

f (x) is even & g (x) is odd

f (0) g (0) - h (0) = ?

\dots \dots \dots \dots \dots \dots

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

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

y (x) + y (- x) = 2 f (x) + h (x) + h (- x)

y (x) - y (- x) = 2 g (x) + h (x) - h (- x)

y (0) + y (0) = 2 f (0) + 2 h (0) \Rightarrow y (0) = f (0) + h (0)

\Rightarrow f (0) + h (0) = 0 \Rightarrow h (0) = - f (0) \dots \dots A

0 = 2 g (0) \Rightarrow g (0) = 0 \dots \dots \dots \dots \dots \dots \dots \dots \dots B

f (0) g (0) - h (0) = f (0) g (0) + f (0)

= f (0) [g (0) + 1]

= f (0) [0 + 1] = f (0)

C o n t i n u e

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

y (x) = x + \sin x

a s s u m e

f (x) = 5 + x^{2} (e v e n)

g (x) = x (o d d)

h (x) = \sin x - 5 - x^{2}

y (x) = f (x) + g (x) + h (x) = \sin x + x

f (0) = 5

g (0) = 0

h (0) = - 5

f (0) g (0) - h (0) = 5

There is no unique answer to given question .

5 was taken as example and can be replaced

by any value .