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常见这道习题:已知f(x+(1/x))=x~2+(1/x~2),求f(x).对其往往采用先配方再换元来求f(x).f(x+(1/x))=x~2+(1/x~2)=(x+(1/x))~2-2.令u=x+(1/x),则f(u)=u~2-2,|u|=|x+(1/x)|=|x|+(1/|x|)≥2.
Commonly used in this exercise: Know that f (x + (1/x)) = x ~ 2 (1/x ~ 2), find f (x). It is often used to formulate and then change the yuan to find f (x) .f(x+(1/x))=x~2+(1/x~2)=(x+(1/x))~2-2. Let u=x+(1/x), then f(u )=u~2-2,|u|=|x+(1/x)|=|x|+(1/|x|)≥2.