Question

Let f be a function such that  .   

.

Solution

Correct option is

We know,   

            

   

                                         [given f (1 + x) = 1 + x (1 + g(x))]  

  

  

  

   

SIMILAR QUESTIONS

Q1

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

Q2

Find the number of points where f (x) = [sin x + cos x(where [.] denotes greatest integral function), x Ïµ [0, 2π] is not continuous.

Q3

  

differentiable function in [0, 2], find a and b. (where [.] denotes the greatest integer function).

Q4

Discuss the continuity of the function .

Q5

Let f : → R, such that f’ (0) = 1 and f (x +2y) = f (x) + f (2y) + ex+2y (x + 2y) – x. ex – 2y. e2y + 4xy∀ xy Ïµ R. Find f (x).

Q6

If g(x) is continuous function in [0, ∞) satisfying g(1) = 1. If

                          .

Q7

Let f is a differentiable function such that 

          .

Q8

Let f : R+ → R satisfies the functional equation  

          .  

If f’(1) = e, determine f (x).

Q9

Let f is a differentiable function such that   

     .

Q10

Find and b so that the function: