It is given that:f(x + y) = f(x) + f(y) ... (i) Putting y = x in the above: f(2x) = 2f(x) Hence, f(
1
2
) = 2f(
1
3
) ...(ii) Also, from equation (i): f(1)=1(
2
3
+
1
3
)=f(
2
3
)+f(
1
3
) =1(
2
3
)+
1
2
f(
2
3
)(from equation (ii) ⇒ f(1)=
3
2
f(
2
3
)orf(
2
3
)=
2
3
f(1) Alternate Solution: Note Hint in such cases the given function f(x) must be a linear function with the constant term zero. Lot f(x) = Kx, where K is a constant, f(1) = K and f(