`f(x) = {(sgn x)^(sgn x)}^n`, n is an odd integer. Determine whether it is odd or even

If f(x) is an odd function,then write whether f'(x) is even or odd.

If f(x) = x^(3) sgn (x), then

If f(x) = x^(3) sgn (x), then

Determine whether the following functions are even or odd. {:((i)f(x)=log(x+sqrt(1+x^(2))),(ii)f(x)=x((a^(x)+1)/(a^(x)-1))),((iii)f(x)=sinx+cosx,(iv)f(x)=x^(2)-abs(x)),((v)f(x)=log((1-x)/(1+x)),(vi)f(x)={(sgn x)^(sgnx)}^(n)," n is an odd integer"):} {:((vii) f(x)=sgn(x)+x^(2),""),((viii)f(x+y)+f(x-y)=2f(x)*f(y)," where " f(0) ne 0 and x","y ne R.,""):}

Determine whether the following functions are even or odd. {:((i)f(x)=log(x+sqrt(1+x^(2))),(ii)f(x)=x((a^(x)+1)/(a^(x)-1))),((iii)f(x)=sinx+cosx,(iv)f(x)=x^(2)-abs(x)),((v)f(x)=log((1-x)/(1+x)),(vi)f(x)={(sgn x)^(sgnx)}^(n)," n is an odd integer"):} {:((vii) f(x)=sgn(x)+x^(2),""),((viii)f(x+y)+f(x-y)=2f(x)*f(y)," where " f(0) ne 0 and x","y ne R.,""):}

If f(x) is an odd function, then write whether f^(prime)(x) is even or odd.

Column I: Function, Column II: Type of function f(x)="{"sgnx")"^(sgn)}; x!=0,n is an odd integer, p. odd function f(x)=x/(e^x-1)+x/2+1 , q. even function f(x)={0,ifxi sr a t ion a l1,ifxi si r r a t ion a l , r. neither odd nor even function. f(x)=max{tanx ,cotx} , s. periodic

Column I: Function, Column II: Type of function f(x)="{"sgnx")"^(sgn)}; x!=0,n is an odd integer, p. odd function f(x)=x/(e^x-1)+x/2+1 , q. even function f(x)={0,ifxi sr a t ion a l1,ifxi si r r a t ion a l , r. neither odd nor even function. f(x)=max{tanx ,cotx} , s. periodic

If f(x) is an even function,then write whether f'(x) is even or odd.