Question

f(x)=x^3-8x-2sinx. state whether the function is odd or even.​

Answer 1

Answer:

$\large\boxed{\sf{Odd\; Function}}$

Step-by-step explanation:

Given a function such that,

$f(x) = {x}^{3} - 8x - 2 \sin(x)$

To find if it is an odd or an even function.

We know that,

For an Odd function,

• f(-x) = -f(x)

For and Even function,

• f(-x) = f(x)

So, now let's find out f(-x)

Therefore, we will get,

$= > f( - x) = {( - x)}^{3} - 8( - x) - 2 \sin( - x) \\ \\ = > f( - x) = - {x}^{3} + 8x - 2( - \sin x) \\ \\ = > f( - x) = - {x}^{3} + 8x + 2 \sin(x) \\ \\ = > f( - x) = - ( {x}^{3} - 8x - 2 \sin x) \\ \\ = > f( - x ) = - f(x)$

Hence, it's an Odd function.