Question

If f(x) = x3 − 3x + sin x + x . cos x, then f(x) + f(−x) = ________​

Answer 1

Answer:

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Answer 2

Given :  

f(x) =  x³ − 3x + sin x + x . cos x

To Find : f(x) + f(−x)

Solution:

f(x) =  x³ − 3x + sin x + x . cos x

f(-x) = (-x)³ − 3(-x) + sin(- x) +(- x) . cos (-x )

Cube of -1 is - 1

Sin(-x) = - Sinx

Cos(-x) = Cosx

=>f(-x) =  -x³ + 3x  - sin x  - x . cos x

=> f(-x) = - ( x³ − 3x + sin x + x . cos x )

=> f(-x)  = - f(x)

=> f(x) + f(-x) = 0

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