Question

se f(x+1) = f(x) + f(1) qualquer x pertence aos reais; f(2)= 1, determinar f(3)

Answer 1

f(x + 1) = f(x) + f(1), sendo f(2) = 1, calcule f(3).

p/x = 1
f(1 + 1) = f(1) + f(1) => f(2) = 2f(1) => 1 = 2f(1) => f(1) = 1/2

p/x = 2 =
f(2 + 1) = f(2) + f(1) => f(3) = f(2) + f(1) => f(3) = 1 + 1/2 => f(3) = (2 + 1)/2

f(3) = 3/2