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___________

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 f(x) be an even function. Then f'(x)

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)=f(x)sinx ,w h e r ef(x) is a twice differentiable function on (-oo,oo) such that f(-pi)=1. The value of |g^n (-pi)| equals __________

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

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

If f(x) is an even function and satisfies the relation x^2dotf(x)-2f(1/x)=g(x),w h e r eg(x) is an odd function, then find the value of f(5)dot

Let f be a function defined on [0,2]. Then find the domain of function g(x)=f(9x^2-1)

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 function and f_(2)(x) is an odd function. Then f_(1)(x+y)+f_(1)(x-y) equals