Questions
If is a polynomial satisfying then is given by
a
63
b
65
c
67
d
68
detailed solution
Correct option is B
Any polynomial satisfying the functional equation f (x) . f (1/x) = f (x) + f (1/x) is of the form xn+1or -xn+1 If 28 =f(3) = -3n+1 then 3n = -27 which is not possible for any n. Hence 28 = f (3) = 3n + 1⇒ 3n= 27 ⇒ n = 3. Thus f (x) = x3 + 1, so f (4) = 43 + 1 = 65.Talk to our academic expert!
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be an even function for all Then the sum of all possible values of a is (where [.] and {.} denote greatest integer function and fractional part function, respectively)
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