Verify assoiativity for the following three mappings : `f: NvecZ_0` (the set of non zero integers), `g: Z_0vecZ` and `h: QvecR` given by `f(x)=2x ,g(x)=1/x` and `h(x)=e^xdot`

Let f(x)=x, g(x)=1//x and h(x)=f(x) g(x). Then, h(x)=1, if

If f@g=g@f, where f(x)=2x+5 and g(x)=3x+h, then: h=

If f: R to R, g , R to R be two funcitons, and h(x) = 2 "min" {f(x) - g(x),0} then h(x)=

(A) For each of the following function f(x), verify that: int_0^2 f(x) dx=int_0^1 f(x) dx+int_1^2 f(x) dx: (i) f(x)=x+2 (ii) f(x)= x^2+2 (iii) f(x)= e^x (B) For each of the following pairs of function f(x) and g(x) , verify that: int_0^1 [f(x)+g(x)]dx=int_0^1 f(x) dx+int_0^1 g(x) dx: (i) f(x)=1,g(x) = x^2 (ii) f(x)=e^x, g(x)=1

If f(x)=4x-5,g(x)=x^(2) and h(x)=(1)/(x) , then f(g(h(x))) is :