The function f(x) is defined for every positive integer x and satisfies the equation f(x+y) = f(x)f(y) - f(xy) + 1 for all positive integers x and y. If f(1) =2, find f(x)?

1 Answer
Jun 1, 2017

f(x)=x+1

Explanation:

Making y=1 we have

f(x+1)=2f(x)-f(x)+1=f(x)+1

or

f(x+1)-f(x) = 1 then

f(x) = x + C_0 but

f(1)=1+C_0=2 rArr C_0=1 and finally

f(x) = x + 1