Let `f(x)a n dg(x)` be two continuous functions defined from `RvecR` , such that `f(x_1)>f(x_2)a n dg(x_1)f(g(3alpha-4))`

If f(x) and g(x) are two continuous functions defined on [-a,a], then the value of int_(-a)^(a){f(x)+f(-x)}{g(x)-g(-x)}dx is

Let f(x) be a continuous function defined from [0,2]rarr R and satisfying the equation int_(0)^(2)f(x)(x-f(x))dx=(2)/(3) then the value of 2f(1)

let f:R rarr R be a continuous function defined by f(x)=(1)/(e^(x)+2e^(-x))

Let f (x) and g (x) be two differentiable functions, defined as: f (x)=x ^(2) +xg'(1)+g'' (2) and g (x)= f (1) x^(2) +x f' (x)+ f''(x). The value of f (1) +g (-1) is:

Let [x] denote the integral part of x in R and g(x)=x-[x]. Let f(x) be any continuous function with f(0)=f(1) then the function h(x)=f(g(x)

Let f(x) be a continuous function defined for 0lexle3 , if f(x) takes irrational values for all x and f(1)=sqrt(2) , then evaluate f(1.5).f(2.5) .

If f(x) and g(x) are continuous functions, then int_(In lamda)^(In (1//lamda))(f(x^(2)//4)[f(x)-f(-x)])/(g(x^(2)//4)[g(x)+g(-x)])dx is

Examine the continuity of the function f defined by f(x)=Lt_(n rarr oo)(x)/((2sin x)^(2x)+1)