If f(x) is a polynomial satisfying f(x) \cdot f(\frac{1}{x})=f(x)+f(\frac{1}{x}) and f(3)=28, then f(4) is given by

NIMCET 2008 Question Paper with solutions

Question : 33 of 120

Marks: +1, -0

f(x)

is a polynomial satisfying

f(x) ⋅ f(\;{1}/{x})=f(x)+f(\;{1}/{x})

and

f(3)=28

, then

f(4)

is given by

Solution:

f(x) ⋅ f(\;{1}/{x})=f(x)+f(\;{1}/{x})

⇒ \;\; f(x)=± x^{n}+1

Given,

\;\; f(3)=28=3^{n}+1

⇒ \;\; 3^{n}=27=3^{3}

⇒ \;\; n=3

⇒ \;\; f(x)=x^{3}+1

⇒ \;\; f(4)=(4)^{3}+1=65

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