the function `f(x)=x/(e^x-1)+x/2+1` is

P.T the real valued function f(x)= (x)/(e^(x)-1) + x/2 + 1 is an even function on R-{0} .

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

Show that the function f(x) = (x - 1) e^(x)+2 is strictly increasing function forall x gt 0 .

The value of k for which the function f(x)=((x)/(e^(x)-1)+(x)/(k)+1) is an even function

Prove that the real valued function f(x)=(x)/(e^(x)-1)+(x)/(2)+1 is an even function on R-{0}

The range of the function f(x)=(e^(x)-1)/(e^(x)+1) is

The function f(x)=1-e^(-x^2/2) is