Question

Let f and g be functions satisfying f(x) = ex g(x), f (x + y) = f (x) + f(y),g(0) = 0, g’(0) = 4 g and g’ are continuous at 0.  

Then

    easy

Solution

Correct option is

             

           

           

  

So f(x) = 4x.

SIMILAR QUESTIONS

Q1

Let f be a twice differentiable function such that f’’(x) = –f(x) and f’(x) = g(x). If h’(x) = [f(x)]2 + [g(x)]2h(1) = 8 and 

h(0) = 2, then h(2) is equal to

Q2

If y2 = P(x) is a polynomial of degree 3, then    

              is equal to  

Q3

If  then the set of all points where the derivative exist is

Q4

The value of y’’ (1) if x3 – 2x2y2 + 5x + y – 5 = 0 when y(1) = 1, is equal to

Q5

If f(x, then f’(1) equals     

 

Q6

 

If f (x) = (1 + x)n, then the value of  

           

Q7

The solution set of f’(x) > g’(x) where f(x) = (1/2)52x + 1 and g(x) = 5x + 4x log 5 is  

Q8

Let f(x) = sin xg(x) = x2 and h(x) = log x.  

Q9

 up to nterms, then y’(0) is equal to

Q10

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