Mr. X is a teacher of mathematics. His students want to know the ages of his son's `S_1` and `S_2`. He told that their ages are `a` and `b` respectively such that `f(x + y) – axy = f(x) + by^2``forall``x,y``inR` after some time students said that information is insufficient, please give more information . Teacher says that `f (1) = 8` and `f (2) = 32 `.
(1) The age of `S_1` will be
(a) `4`
(b) `8`
(c) 16
(d) 32

(2) The function `f(x)` is
(a) even
(b) odd
(c) neither even nor odd
(d) periodic as well as odd

(3) The age of `S_2` will be
(a) `4`
(b) `8`
(c) 16
(d) 32