Question

If f(3x)=f(3) + f(x) then show that f(1)-f(3)-f(9) -f(27) = f (81).​

Answer 1

The claim is wrong, or your question is incorrectly entered.

`x=1 \implies f(3) = f(3) + f(1) \implies f(1) = 0`

`x=3 \implies f(9) = f(3) + f(3) = 2f(3)`

`x=9 \implies f(27) = f(3) + f(9) = 3 f(3)`

`x=27 \implies f(81) = f(3) + f(27) = 4f(3)`

Then

`f(1) - f(3) - f(9) - f(27) = 0 - f(3) - 2f(3) - 3f(3) = -6f(3) \\eq 4f(3) = f(81)`

at least if
`f(3)\\eq0`.