Question

If f(x)=3cosx + x (sinx) +1 show that f(x) is even or odd function

Answer 1

Answer:

$\large\bold\red{Even\: function}$

Step-by-step explanation:

Given,

$f(x) = 3 \cos(x) + x \sin(x) + 1$

Therefore,

We get,

$= > f( - x) = 3 \cos( - x) + ( - x) \sin( - x) + 1$

But,

We know that,

• $\cos( - x) = \cos(x)$
• $\sin( - x) = - \sin(x)$

Therefore,

We get,

$= > f( - x) = 3 \cos(x) + x \sin(x) + 1$

Clearly,

We have,

$f(x) = f( - x)$

Hence,

It's an even function.