Question

if f(xy)=f(x)+f(y)
find f(1) and f(-1)

Answer 1

\[f(1)=f(1\times 1)\] is a start

Answer 2

but why is this so?

Answer 3

? because \(1\times 1=1\)

Answer 4

the point being that since \(f(xy)=f(x)+f(y)\) then you know \[f(1)=f(1\times 1)=f(1)+f(1)\] subtracting \(f(1)\) from both sides indicates \(f(1)=0\)

Answer 5

oh! thank you my eyes are open now