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SIMILAR QUESTIONS

Q1

 

Let f is a differentiable function such that 

            .

Q2

 

Let f : R+ → R satisfies the functional equation  

          .  

If f’(1) = e, determine f (x).

Q3

 

Let f is a differentiable function such that   

     .

Q4

 

Let f be a function such that  .   

.

Q5

 is continuous at x = 0, find the values of Aand B. Also find f (0).

Q6

Determine the form of g(x) = f (f (x)) where f (x and hence find the point of iscontinuity of g, if any.

Q7

Find the natural number a for which  where the function f satisfies the relation f (x + y) = f (xf (y) for all natural number xy and further f (1) 2.

Q8

Find the derivative of y = log x wrt x from first principles.