Question

 

Solution

Correct option is

Putting     x = y = 0,       we get         f (0) = 0  

Putting     y = – x,           we get         f (+x) + f (–x) = f (0)  

⇒      f (–x) = – f (x)                                      …(ii)  

  

                      

           

   

   

Integrating both sides, 

         

  

Thus f (x) = 2 tan-1x  

  

SIMILAR QUESTIONS

Q1

Let f : R → R be a function defined by f (x) =  max. {xx3}. The set of all points where (x) is not differentiable is:

Q2

Let f (x) = Ï•(x) + ψ(x) and Ï•(a), ψ’(a) are finite and definite. Then:

Q3

If f (x) = x + tan and g(x) is the inverse of f (x) then g’ (x) is equal to:

Q4

If f (x) is differentiable function and (f (x). g(x)) is differentiable at x = a, then

Q5

        

Determine the value of ‘a’ if possible, so that the function is continuous

Q6

 for all real x and y. If f ’ (0) exists and equals to –1and f (0) = 1, find f ’(x).

Q7

Now if it is given that there exists a positive real δ, such that f (h) = h for 0 < h < δ then find f’(x) and hence f (x).

Q8

Let f  be an even function and f ’(0) exists, then find f’(0).

Q9

Let f (x) = xnn being non-negative integer. Then find the value of n for which the equality f’(a + b) = f ’(a) + f ’ (b) is valid for all, ab > 0

Q10

Find the set of points where x2 |x| is true thrice differentiable.