the answer is 8001

for any function like

f(x) . f(1/x) = f(x)  + f(1/x)

f(x) =

here n = 3

as f(10) = 1 + (10)^3 = 1001

so for f(20) = 1+ (20)^3 = 8001

How dids you get this that if f(x) . f(1/x) = f(x) + f(1/x), then

f(x) = 1+-x^n.

Please explain.



 

Put  x = 1

----------------------------------------------(1)

Now

Comparing to eqn. (1)   we can see that equation is f(x) = something + 1

ALSO GIVEN F(10) = 1001 = 1000 + 1 = 10^3 + 1  .......................trying to write expression in terms of what we chose as x.

so similarly we see that f(1) = 2 = 1^3 + 1

So

But for the method you're using shouldn't it be given in the question that the function is a polynomial? I don't think you can use it otherwise..

well gaurav

this methd is gud par its i thnk will be gud for objective exams.......

i dunno know whether its gud subj ans......

hmm....... is der any other way of solving this???

for any function like

f(x) + f(1/x) = f(x).f(1/x)

f(x)= 1+-x^n

Now applying this case

f(10)=1+10^3=1001

f(20)=1+20^3=8001

so the required answer is 8001