设f(1/x)=x/1-x^2,则f(x)=,f(√2-1)=如题

Question

设f(1/x)=x/1-x^2,则f(x)= ,f(√2-1)=如题

Answer 1

令1/x=t,则 x=1/t,得f(t)=x/(1-x^2)=(1/t)/[1-(1/t)^2]=t/(t^2-1),故f(x)=x/(x^2-1),f(√2-1)=(√2-1)/[(√2-1)^2-1]=(√2-1)/(2-2√2)=--1/2.