Question:

Let f : be a continuous function such that f(1) ≠ 0

And

f (x + y) = f (x) + f (y) for all x , y

a) Prove that f (0) = 0

b) Prove that f (-x) = - f(x) for all x .

c) Define a = f (1). Prove that \(f\left( n \right)=na\) for every integer n

d) Prove that f ( for every integer m , m ≠ 0. Conclude that

f (r) = ra for every rational r

e) Prove that f(x) = ax for all x