If `f(x)` is an even function and f'(x) exist for all x then `f'(1)+f'(-1)` is

If int(x^(2)-x+1)/((x^(2)+1)^((3)/(2)))e^(x)dx=e^(x)f(x)+c, then 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

Let f (x) = a ^ x ( a gt 0 ) be written as f ( x ) = f _ 1 (x ) + f _ 2 (x) , where f _ 1 ( x ) is an even function and f _ 2 (x) is an odd function. Then f _ 1 ( x + y ) + f _ 1 ( x - y ) equals :

If f(x)=x*x 1) and f'(x) exists finitely for all x in R, then

f (x) is any function and f^(-1)(x) is known as inverse of f (x) , then f^(-1)(x) of f(x)=(1)/(x)+1 is

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.

If f(x) is a function such that f(xy)=f(x)+f(y) and f(3)=1 then f(x) =

If f(x) is a function such that f(xy)=f(x)+f(y) and f(3)=1 then f(x)=

Let f(x) be a differentiable function for all x in R The derivative of f(x) is an even function If the period of f(2x) is 1 then the value of f(2)+f(4)-f(6)-f(8) is.

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1+x) then (1) g(x) is an odd function (2)g(x) is an even function (3) graph of f(x) is symmetrical about the line x=1 (4) f'(1)=0