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Kapil Khare
80 Points
2 years ago
Since, the given relation is true for all x and y then we can put any real value in place of x and y.

Put x = y = 1, then
f(2) – a = f(1) + b
$\implies$                        32 – 8 = a + b
$\implies$                          a + b = 24

Put x=1 and y=0, then
f(1) – a = f(1)
$\implies$                                a = 0
$\implies$                                b = 24

$\implies$                      f(x+y) = f(x) + 24y2

Put x=0 and y=1, then
f(1) = f(0) + 24
$\implies$                      f(0) = –16

Put  y=z and x = 0, then
f(z) = f(0) + 24z2
$\implies$                       f(z) = 24z2 – 16

A) The age of S1 = a = 0
The age of S2 = b = 24

​B) The function f(x) = 24x2 – 16