The function `f(x)=(x+1)/(x^3+1)` can be written as the sum of an even function `g(x)` and an odd function `h(x)` . Then the value of `|g(0)|` is___________

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 -

If f(x) + g(x) = e^(-x) where f(x) is an even function and g(x) is an odd function then f(x) =

[" 8.Let "f(x)=a^(1)(a>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 the "g(x+y)+g(x-y)" is "],[[" A) "2g(x)g(y)," B) "2g(x+y)g(x-y)],[" C) "2g(x)," D) "g(x)-g(y)]]

If the function f(x)=x^3+e^(x/2) and g(x)=f ^(−1)(x) , then the value of g ′ (1) is

If f(x) is an even function and g is an odd function, then f(g(x)) is……………….function

If the function f(x)= x^(3)+e^(x/2) and g(x) = f^(-1)(x) then the value of g^(')(1) is

If the function f(x) = x^3 + e^(x/2) and g(x) =f^-1(x) , then the value of g'(1) is

Statement-1: Every function can be uniquely expressed as the sum of an even function and an odd function. Statement-2: The set of values of parameter a for which the functions f(x) defined as f(x)=tan(sinx)+[(x^(2))/(a)] on the set [-3,3] is an odd function is , [9,oo)