If f(x+y)= f(x)*f(y) for all values of x,y belongs to R. Find possible value of f(0) if f(0) > 0

Question

Its about reformation property of a fucntion. 

Answer 1

Try working with x = y = 0

 

f(0) = f(0 + 0) = f(0)f(0) ⇒

 

f(0) = f(0)²

 

f(0) = 0 or 1

 

If f(0) > 0, then f(0) = 1