Let $f : R - {0} \to R$ be a function which is differentiable in its domain and satisfying the equation $f (x + y) = f (x) + f (y) + \frac{x + y}{x y} - \frac{1}{x + y},$ also f'(1)=2. Then find the function.

Views: 750 students

Found 3 tutors discussing this question

Elizabeth Discussed

Let

f : R - {0} \to R

be a function which is differentiable in its domain and satisfying the equation

f (x + y) = f (x) + f (y) + \frac{x + y}{x y} - \frac{1}{x + y},

also f'(1)=2. Then find the function.

12 mins ago

Discuss this question LIVE

12 mins ago

Question Text

Let

f : R - {0} \to R

be a function which is differentiable in its domain and satisfying the equation

f (x + y) = f (x) + f (y) + \frac{x + y}{x y} - \frac{1}{x + y},

also f'(1)=2. Then find the function.

Filo tutor solution