Limits

g (x). g(y) = g(x) + g (y) + g (x y) - 2 ...(1)
Put x = 1, y = 2, then
g (1). g(2) = g (1) + g (2) + g (2) - 2
5g (1) = g (1) + 5 + 5 - 2
4g (1) = 8 g(1) = 2
Put y = in equation (1) , we get
g(x).g =g(x) +g g(1) -2
g(x).g =g(x) +g +2 -2
[ g(1) = 2 ]
This is valid only for the polynomial
g (x) = 1 x ... (2)
Now g (2) = 5 (Given)
1 2n = 5 [Using equation (2)]
2 = 4, 2 = 4, -4
Since the value of 2 cannot be -Ve.
So, 2 = 4, n = 2
Now, put n = 2 in equation (2), we get
g (x) = 1 + x
\rightarrow g(x) = \rightarrow (1 x ) =1 (3)
=1 9 = 10, - 8