An algebra problem by abhishek anand

Algebra Level 4

f ( x ) ⋅ f ( 1 x ) = f ( x ) + f ( 1 x ) f(x)\cdot f\left(\frac{1}{x}\right)=f(x)+f\left(\frac{1}{x}\right) and it is given that f ( 3 ) = 28 f(3)=28 .

Find the value of f ( 8 ) f(8) .


The answer is 513.

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Abhishek Anand by abhishek anand , 20, India

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1 solution

Pawan Pal
Apr 4, 2016

Easy one .. Write f(x) as a and find f(1/x) in terms of a . From f(3) find f(1/3) it would be 28/27. We know f(1/x) = a/a-1 Compare this with 28/26 u find that a is basically x^3 +1 . so for f(8) x=8 I.e 8^3 + 1 = 512+1= 513. I hope u guys understand this solution. I m not used to latex :(

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