Let `f:""(-1,""1) rarr R` be a differentiable function with `f(0)""=""-1" "a n d" "f'(0)""=""1` . Let `g(x)""=""[f(2f(x)""+""2)]^2` . Then `g'(0)""=` (1) `-4` (2) 0 (3) `2` (4) 4

Let f:""(1,""1)vecR be a differentiable functio with f(0)""=""-1""a n d""f'(0)""=""1 . Let g(x)""=""[f(2f(x)""+""2)]^2 . Then g'(0)""= (1) 4 (2) 0 (3) 2 (4) -4

Let f : (-5,5)rarrR be a differentiable function of with f(4) = 1, f'(4)=1, f(0) = -1 and f'(0) = If g(x)=(f(2f^(2)(x)+2))^(2), then g'(0) equals

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then f(x) is

Let f : R rarr R : f(x) = (2x-3)/(4) be an invertible function. Find f^(-1) .

Let f be differentiable function such that f'(x)=7-3/4(f(x))/x,(xgt0) and f(1)ne4" Then " lim_(xto0^+) xf(1/x)

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

Let f(x) be a twice-differentiable function and f''(0)=2. Then evaluate lim_(xto0) (2f(x)-3f(2x)+f(4x))/(x^(2)).

Let f : R rarr R be a differentiable function at x = 0 satisfying f(0) = 0 and f'(0) = 1, then the value of lim_(x to 0) (1)/(x) . sum_(n=1)^(oo)(-1)^(n).f((x)/(n)) , is

STATEMENT - 1 : Let f be a twice differentiable function such that f'(x) = g(x) and f''(x) = - f (x) . If h'(x) = [f(x)]^(2) + [g (x)]^(2) , h(1) = 8 and h (0) =2 Rightarrow h(2) =14 and STATEMENT - 2 : h''(x)=0