Let `f:[0'1] to [-1,1]` and `g:[-1,1] to [0,2]` be two functions such that g is injective and `g^(@) f:[0,1] to [0,2]` is surjective. Then

Let f:[0.1] rarr[0,1] and g:[0,1] rarr[0,1] be two functions defined by f(x)=(1-x)/(1+x) and g(x)=4 x(1-x) , then f . o g(x)=

Let f: [0, 1] to [1, 2] defined as f(x) = 1 + x and g : [1, 2] to [0, 1] defined as g(x) = 2 – x then the composite function gof is

Let f : (-1,1) to R be a differentiable function with f(0) =-1 and f'(0)=1 Let g(x)= [f(f(2x)+1)]^2 . Then g'(0)=

Let f (x) and g (x) be two differentiable functions for 0 le x le 1 such that f (0) = 2, g (0) = 0,f (1) = 6. If there exists a real number c in (0,1) such that f'(c ) = 2 g '(c ) , then g (1) is equal to

Let f,g : [-1,2] to be continuous functions which are twice differentiable on the interval (-1,2). Let the values of f and g at the points and 2 be as given in the following table: In each of the intervals (-1,0) and (0, 2) the function (f-3g) never vanishes. Then the correct statements(s) is(are) :

Let f : (-1,1) to R be a differentiabale function with f(0) = -1 and f'(0) = 1. Let g(x) = [f(2f(x)+2)]^(2) , then g'(0)=