Thread: need help for proof with simple function

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