If ` f:RR-> RR ` is a differentiable function such that `f(x) > 2f(x) ` for all `x in RR ` and `f(0)=1, ` then

Let f:RR to RR,g:RR to RR and h:RR to RR be differentiable functions such that f(x)=x^(3)+3x+2,g(f(x))=x and h(g(g(x)))=x for all x in RR . Then,

Let F:RR to RR be a thrice differentiable function. Suppose that F(1)=0,F(3)=-4 and F'(x)lt0 for all x in(1,3) . Let f(x)=xF(x) for all x in RR . If int_(1)^(3)x^(2)F'(x)dx=-12 and int_(1)^(3)x^(3)F''(x)dx=40 , then the correct expression(s) is(are)-

Let F:RR to RR be a thrice differentiable function. Suppose that F(1)=0,F(3)=-4 and F'(x)lt0 for all x in((1)/(2),3) . Let f(x)=xF(x) for all x in RR . The correct statement(s) is (are)-

If f:RR to RR satisfies f (x+y) =f (x) + f (y) for all x,y in RR and f(1) =7, then the value of sum _(r=1) ^(n) f(r) is-

Let f:RR to(0,oo)" and "g:RR to RR be twice differentiable functions such that f'' and g'' are continuous functions on RR . Suppose f'(2)=g(2)=0,f''(2)ne0 and g'(2)ne0 . If underset(x to2)lim(f(x)g(x))/(f'(x)g'(x))=1 . Then

Let f:RR rarr RR and g: RR rarr RR be two functions such that (g o f) (x) = sin ^(2) x and ( f o g) (x) = sin (x^(2)) . Find f(x) and g(x) .

If the function f: R to R is defined by f(x) =(x^(2)+1)^(35) for all x in RR then f is

Let RR be the set of real numbers and f: RR rarr RR ,g: RR rarr RR be two functions such that, (g o f) (x) = 4x^(2)+4x+1 and (f o g ) (x) = 2x^(2)+1 . Find f(x) and g(x) .

Let f: RR rarr RR be a function defined by f(x)=ax+b , for all x in RR . If (f o f)=I_(RR) Find the value of a and b.