Suppose that `f(x)f(f(x))=1` and `f(1000)=999` then which of the following is true a)f(500)-1/500 b)f(199)=1/199 c)f(1999)=1/1999 d)f(x)=x

If f'(x) = sqrt(x) and f(1) = 2 then f(x) is :

Let f(x) be a twice differentiable function for all real values of x and satisfies f(1)=1,f(2)=4,f(3)=9. Then which of the following is definitely true? (a). f''(x)=2AAx in (1,3) (b) f''(x)= 5 for some x in (2,3) (c) f''(x)=3AAx in (2,3) (d) f''(x)=2 for some x in (1,3)

If f(x)=xtan^(-1)x , then f'(1) is

Which of the following function from Z to itself are bijections? f(x)=x^3 (b) f(x)=x+2 f(x)=2x+1 (d) f(x)=x^2+x

If f''(x)=12x-6 and f(1)=30, f'(1)=5 find f(x) .

IF f(x) =2x^2 +bx +c and f(0) =3 and f (2) =1, then f(1) is equal to

If f''(x) = 12x - 6 and f(1) = 30 , f' (1) = 5 find f(x)

If f''(x) = 12 x - 6 and f(1) = 30 , f'(1) = 5 find f (x) .

If f'(x)=f(x)+int_(0)^(1)f(x)dx ,given f(0)=1 , then the value of f(log_(e)2) is

If R->R is an invertible function such that f(x) and f^-1(x) are symmetric about the line y=-x, then (a) f(x) is odd (b) f(x) and f^-1(x) may be symmetric (c) f(c) may not be odd (d) non of these