1.混淆复合函数的反函数与反函数的复合函数例1已知f(x)=x2(x≤0),求f-1(x+1).误解∵f(x)=x2(x≤0),∴f(x+1)=(x+1)2(x≤-1),令y=f(x+1),即y=(x+1)2,解得x=-1±y,∵x≤-1,∴x=-1-y,∴f-1(x+1)=-1-x(x≥0).剖析误认为f-1(x+1)是f(x+1)的反函数,而事实上f-1(x+1)是反函数的复合函 1. Mix function of inverse function and inverse function of mixed compound function Example 1 Given that f(x)=x2(x≤0), find f-1(x+1). Misunderstood ∵f(x)=x2(x ≤ 0), ∴f(x+1)=(x+1)2(x≤-1), let y=f(x+1), ie y=(x+1)2, solve x=- 1±y, ∵x≤-1, ∴x=-1-y, ∴f-1(x+1)=-1-x(x≥0). The analysis mistakes that f-1(x+1) is The inverse function of f(x+1), and in fact f-1(x+1) is a compound function of the inverse function