If `f: RrarrR and g:RrarrR` are two given functions, then prove that `2min.{f(x)-g(x),0}=f(x)-g(x)-|g(x)-f(x)|`

If f(x) and g(x) are two real functions such that f(x)+g(x)=e^(x) and f(x)-g(x)=e^(-x) , then

If g is inverse of f then prove that f''(g(x))=-g''(x)(f'(g(x)))^(3).

If g is inverse of f then prove that f''(g(x))=-g''(x)(f'(g(x)))^(3).

Let f: RrarrR and g: RrarrR be two functions such that fog(x)=sinx^2 and gof(x)=sin^2x Then, find f(x) and g(x)dot

If f(x) =x^(2)andg(x)=2x+1 are two real valued function, then evaluate : (f+g)(x),(f-g)(x),(fg)(x),(f)/(g)(x)

Prove that int_(0)^(a)f(x)g(a-x)dx=int_(0)^(a)g(x)f(a-x)dx .

If f(x)=log_(e)x and g(x)=e^(x) , then prove that : f(g(x)}=g{f(x)}

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)=

Let f(x) and g(x) be real valued functions such that f(x)g(x)=1, AA x in R."If "f''(x) and g''(x)" exists"AA x in R and f'(x) and g'(x) are never zero, then prove that (f''(x))/(f'(x))-(g''(x))/(g'(x))=(2f'(x))/(f(x))

If g is the inverse function of and f'(x) = sin x then prove that g'(x) = cosec (g(x))