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) is an odd function, f(1)=3,f(x+2)=f(x)+f(2), then the value of f(3) is________

If f(x) is an odd function, f(1)=3,f(x+2)=f(x)+f(2), then the value of f(3) is________

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 invertible function and g(x)=2f(x)+5, then the value of g^(-1)(x)i s

The function f(x)=sin(log(x+sqrt(1+x^2))) is (a) even function (b) odd function (c) neither even nor odd (d) periodic function

Let G(x)=(1/(a^x-1)+1/2)F(x), where a is a positive real number not equal to 1 and f(x) is an odd function. Which of the following statements is true? (a) G(x) is an odd function (b) G(x)i s an even function (c) G(x) is neither even nor odd function. (d)Whether G(x) is an odd or even function depends on the value of a

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

If f(x)={x^2sin((pix)/2),|x|<1x|x|,|x|geq1,t h e nf(x)i s an even function (b) an odd function a periodic function (d) none of these

In the function f(x) is defined for x in[0,1] then the function f(2x+3) is defined for