A function [tex]f(x)[/tex] is odd, when [tex]f(-x)= -f(x)[/tex] and even when [tex]f(-x)= f(x)[/tex]
21. Given function: [tex]y= 1- cos(x)[/tex] or [tex]f(x)= 1-cos(x)[/tex]
So, [tex]f(-x)= 1-cos(-x) = 1- cos(x) = f(x)[/tex]
As here [tex]f(-x)= f(x)[/tex], so the function will be Even function.
23. Given function: [tex]y=f(x)= \frac{x^4 +1}{x^3-2x}[/tex]
So, [tex]f(-x)= \frac{(-x)^4 +1}{(-x)^3 -2(-x)}= \frac{x^4 +1}{-x^3+2x}=\frac{x^4+1}{-(x^3-2x)}=-\frac{x^4+1}{x^3-2x}=-f(x)[/tex]
As, here [tex]f(-x)= -f(x)[/tex], so the function will be Odd function.
