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if f(x).f(1/x) = f(x) + f(1/x) then prove that f(x) = x n + 1

if f(x).f(1/x) = f(x) + f(1/x) then prove that f(x) = xn+ 1

Grade:12th pass

2 Answers

Sourabh Singh IIT Patna
askIITians Faculty 2104 Points
6 years ago
Hii
you can find out the value of f(x) and f(1/x) .
Multilply f(x) and f(1/x) and then add f(x) and f(1/x).
So both these values will be equal.


rishabh
30 Points
6 years ago
In this question.. It must be given that the function is a polynomial(which is indirectly given to be proved).. So take a general polynomial of degree n and then subsitute that in the given equation.. Then compare both sides coefficient then you will get the proof

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