Question

已知f(x)是一次函数,且f-1{f-1[f-1(x)]}=8x+7,求f(x)的解析式

Answer 1

设,f(x)的反函数为:f-(x)=aX+b,则有

f-1[f-1(x)]=a[f-1(x)]+b=a^2x+ab+b.

f-1{f-1[f-1(x)]=a^2[f-1(x)]+ab+b=a^2(ax+b)+ab+b=a^3x+a^2b+ab+b

=8x+7.

a^3=8,a^2b+ab+b=7.

a=2,b=1.

∴f-(x)=2x+1,f-(x)的反函数为X=[f-1(x)-1]/2.

∴f(x)=(x-1)/2.