`f(x)=h(x)+h(-x)+x^2cotx` is an even function

Let f(x)=a^(x)(a gt 0) be written as f(x)=g(x)+h(x) where g(x) is an even function and h(x) is an odd function. Then the value of g(x+y)+g(x-y) is -

Let f be a real function. Show that h(x) =f(x)=f(-x) is always an even function and g(x) = f(x) -f(-x) is always an odd fuction.

If int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^xf(x)+c ,t h e n f(x) is an even function f(x) is a bounded function the range of f(x) is (0,1) f(x) has two points of extrema

If f(x)=(cosx+ sinx)/(tanx+cotx) then function f(x) is

Let f(x)=e^(e^(|x|sgnx))a n dg(x)=e^(e^(|x|sgnx)),x in R , where { } and [ ] denote the fractional and integral part functions, respectively. Also, h(x)=log(f(x))+log(g(x))dot Then for real x , h(x) is (a)an odd function (b)an even function (c)neither an odd nor an even function (d)both odd and even function

Let f(x)=e^(e^(|x|sgnx))a n dg(x)=e^(e^(|x|sgnx)),x in R , where { } and [ ] denote the fractional and integral part functions, respectively. Also, h(x)=log(f(x))+log(g(x))dot Then for real x , h(x) is (a)an odd function (b)an even function (c)neither an odd nor an even function (d)both odd and even function

Let h(x)=(x)/(5^(x)-1)+(x)/(2)+5 then h(x) is (1) Even Function (2) Odd Fucntion (3) Neither even nor odd (4) Periodic Function

Statement 1: If f(x) is an odd function,then f'(x) is an even function.Statement 2: If f'(x) is an even function,then f(x) is an odd function.

Statement - I : If f(x) is an odd function, then f'(x) is an even function. Statement - II : If f'(x) is an even function, then f(x) is an odd function.