Home
Class 12
MATHS
Let f(x+y) = f(x) + f(y) - 2xy - 1 for a...

Let `f(x+y) = f(x) + f(y) - 2xy - 1` for all x and y. If f'(0) exists and `f'(0) = - sin alpha`, then `f{f'(0)}` is

A

-1

B

0

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
Doubtnut Promotions Banner Mobile Dark
|

Similar Questions

Explore conceptually related problems

Let f((x+y)/2)=(f(x)+f(y))/2 for all real x and y. If f'(0) exists and equals -1 and f(0)=1, find f(2)

Let f be an even function and f'(0) exists, then f'(0) is

Knowledge Check

  • f(x+ y) = f(x) f(y) , For AA x and y . If f(3)= 3 and f'(0) =11 then f'(3)= …….

    A
    22
    B
    44
    C
    28
    D
    None of these

    • Similar Questions

    Explore conceptually related problems

    If f((x)/(y))=(f(x))/(f(y)) for all x, y in R, y ne 0 and f'(x) exists for all x, f(2) = 4. Then, f(5) is

    A function f:R->R satisfies the relation f((x+y)/3)=1/3|f(x)+f(y)+f(0)| for all x,y in R. If f'(0) exists, prove that f'(x) exists for all x, in R.

    Let f(x+y)=f(x)+f(y)+2x y-1 for all real xa n dy and f(x) be a differentiable function. If f^(prime)(0)=cosalpha, the prove that f(x)>0AAx in Rdot

    Let f(x) and g(x) be functions which take integers as arguments. Let f(x + y) =f(x)+ g(y) + 8 for all intege x and y. Let f(x) = x for all negative integers x and let g (8) = 17 . Find f(0).

    If f(x) + f(y) = f((x+y)/(1-xy)) for all x, y in R (xy ne 1) and lim_(x rarr 0) (f(x))/(x) = 2 , then

    Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is continuous at x=0, show that f(x) is continuous for all xdot

    A function f (x) is defined for all x in R and satisfies, f(x + y) = f (x) + 2y^2 + kxy AA x, y in R , where k is a given constant. If f(1) = 2 and f(2) = 8 , find f(x) and show that f (x+y).f(1/(x+y))=k,x+y != 0 .

    Home
    Profile