Question

21 and 23 please explained

Answer 1

A function
`f(x)` is odd, when
`f(-x)= -f(x)` and even when
`f(-x)= f(x)`

21. Given function:
`y= 1- cos(x)` or
`f(x)= 1-cos(x)`

So,
`f(-x)= 1-cos(-x) = 1- cos(x) = f(x)`

As here
`f(-x)= f(x)`, so the function will be Even function.

23. Given function:
`y=f(x)= (x^4 +1)/(x^3-2x)`

So,
`f(-x)= ((-x)^4 +1)/((-x)^3 -2(-x))= (x^4 +1)/(-x^3+2x)=(x^4+1)/(-(x^3-2x))=-(x^4+1)/(x^3-2x)=-f(x)`

As, here
`f(-x)= -f(x)`, so the function will be Odd function.