FunctionHard
Question
If g(x) is a polynomial satisfying g(x) g(y) = g(x) + g(y) + g(xy) - 2 for all real x and y and g(2) = 5 then g(3) is equal to -
Options
A.10
B.24
C.21
D.none of these
Solution
g(x) g(y) = g(x) + g(y) + g(xy) - 2
put x = 2 & y = 1
g(2) g(1) = g(2) + g(1) + g(2) - 2
⇒ 4g(1) = 8 g(1) = 2
g(x) g(y) = g(x) + g(y), now put y =
Now g(x) g
= g(x) + g
g(x) = 1 ± xn
∴ 5 = 1 ± 2n (∵ g(2) = 5)
so, n = 2
Now g(3) = 1 + 32 = 10
put x = 2 & y = 1
g(2) g(1) = g(2) + g(1) + g(2) - 2
⇒ 4g(1) = 8 g(1) = 2
g(x) g(y) = g(x) + g(y), now put y =
Now g(x) g
= g(x) + gg(x) = 1 ± xn
∴ 5 = 1 ± 2n (∵ g(2) = 5)
so, n = 2
Now g(3) = 1 + 32 = 10
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