一、拼凑法形如f[h(x)]=g(x)的结构,通过对g(x)进行观察、分析、变形,转化为关于h(x)的多项式,用x替换h(x)即得函数的解析式.例1已知函数f(x)满足:f(x-x1)=x2+x12,求f(x).解∵f(x-x1)=x2+x12=(x-1x)2+2,∴设x-x1=t,则有f(t)=t2+2.∴f(x)=x2+2.二、换元法形如f[h(x)]=g(x)的结构 First, put together a structure such as f[h(x)]=g(x), by observing, analyzing, and deforming g(x), transforming it into a polynomial about h(x), replacing h with x (x ) That is, the analytical expression of the function. Example 1 Known function f(x) satisfies: f(x-x1)=x2+x12, find f(x). Solution ∵f(x-x1)=x2+x12=( X-1x)2+2, set x-x1=t, then there is f(t)=t2+2.∴f(x)=x2+2. Two, the modifiation method is like f[h(x) ]=g(x) structure