Let `f(x)=x^(2)` and `g(X)=sinx` for all `xepsilonR`. Then the set of all `x` satisfying `(f o g o g o f)(x)=(g o g o f)(x)`, where `(f o g)(x)=f(g(x))`is

Let f(x) = e^(x) - x and g (x) = x^(2) - x, AA x in R . Then the set of all x in R where the function h(x) = (f o g) (x) in increasing is :

Let f:ZtoZ:f(x)=x^(2)andg:ZtoZ:g(x)=|x|^(2)" for all "x""inZ . Show that f=g.

Let f(x)=sin((pi)/6sin((pi)/2 sin x)) for all x epsilonR and g(x)=(pi)/2sinx for all x epsilonR . Let (fog) (x) denote f(g(x)) and (g o f) denote g(f(x)). Then which the following is (are) true?

If f(x)=x^2 and g(x)=x^2+1 then: (f@g)(x)=(g@f)(x)=

If f(x)=1+2x and g(x) = x/2 , then: (f@g)(x)-(g@f)(x)=

let f(x)=sqrt(x) and g(x)=x be function defined over the set of non negative real numbers. find (f+g)(x),(f-g)(x),(fg)(x) and (f/g)(x)

Let f(x) = x^(2) and g(x) = 2x + 1 be two real functions. Find : (f + g) (x), (f - g) (x), (fg) (x) and ((f)/(g)) (x) .

Let f : R to R : f (x) =x^(2) " and " g: R to R : g (x) = (x+1) Show that (g o f) ne (f o g)

If f'(x)=g(x) and g'(x)=-f(x) for all x and f(2)=4=f'(2) then f''(24)+g''(24) is