a)

to prove f(0) = 0

f(x + y) = f(x) + f(y)

put x = y =0

we get

f(0 + 0) = f(0) + f(0)

=> f(0) = 2f(0)

=> f(0) = 0

b)f(n) = f(1 + (n-1))

= f(1) + f(n-1)

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

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

and so on

= f(1) + f(1) + f(1) + f(1) + f(1) --- ntime

= nf(n)

you can also use mathematical induction for proving part b of problem