Question

已知f(x+1/x)=x^2+1/x^2求f(x)

求几种方法

Answer 1

f(x+1/x)=x^2+1/x^2,
令x+1/x=t
则有:
x^2+1/x^2=(x+1/x)^2-2
=t^2-2
所以
f(t)=t^2-2
f(x)=x^2-2

f(x+1/x)=(x+1/x)^2-2,
把x+1/x看做一个自变量t，
则可得f(t)=t^2-2,
别忘了定义域，
t=x+1/x 属于 (负无穷大,-2],[2,正无穷大)

Answer 2

f(x+1/x)=x^2+1/x^2
=x^2+1/x^2+2-2
=(x+1/x)^2-2
so
f(x)=x^2-2