I really don't know what to do for part a. Help with b would be nice, too.
Thanks.
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