Question
If f(x) is a polynomial function satisfying the condition f(x). f(1/x) = f(x) + f(1/x) and f(2) = 9 then -
- 2 f(4) = 3f(6)
- 14 f(1) = f(3)
- 9 f(3) = f(5)
- f(10)= f(11)
Hint:
The correct answer is: 14 f(1) = f(3)
To choose the correct option from the given function.
The polynomial which satisfies f(x)f(1/x)=f(x)+f(1/x) is ±
Given, f(2)=9
± =9
n=3
Hence the function is f(x)=
f(3)=28, f(1)=2
14 x f(1) = f(3)
14 x 2 = 28
28 = 28
Given, f(2)=9
Hence the function is f(x)=
Therefore, 14 f(1) = f(3)
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