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
Create a free account to view solution
View Solution FreeMore Function Questions
If f(x + ay, x − ay ) = axy, then f (x,y) equals-...Let E = {1, 2, 3, 4} and F = {1, 2}, Then, the number of onto functions from E to F is...Let f(x) = in x & g(x) = . The domain of f(g(x)) is -...Range of the function f(x) = cos (K sin x) is [-1 , 1] , then the least positive integral value of K will be -...The function f(x) = , x > 0 is -...