Question

let f(x+1/x)=x^2+1/x^2,x does not =0, then find f(x)​

Answer 1

We are given

f(x+2 )=x^2 + x^2+1

(where x=0)=x^2 +x^2+1 +2−2

=x^2 + x ^21+2(x^2)( x ^2+1)−2.

f(x+x )=(x+x^2) −2

So, simply put x+x1

we get ( x ) = x^2-2