Question

What is even and odd function?

Answer 1

Even and odd function:

• Even function: function,$f\left(x\right)$ is said to be even if it satisfies the condition$f\left(x\right)=f(-x)$. For example, the trigonometric function $f\left(x\right)=\cos x$is an even function.

Other examples of even functions are $x^2,x^4,x^6,x^{12}..$ etc.

• Odd function: A function,$f\left(x\right)$ is said to be odd if it satisfies the condition$f(-x)=-f\left(x\right)$. For example, the trigonometric function $f\left(x\right)=\sin x$is odd.

Other examples of an odd function are $x,x^3,x^5,x^{45}..$etc.

Thus, a function$f\left(x\right)$ is said to be even if it satisfies the condition$f\left(x\right)=f(-x)$, and a function$f\left(x\right)$ is said to be odd if it satisfies the condition$f(-x)=-f\left(x\right)$.