Question

已知f(x)是一次函数,且f(f(x))=16x-25,

Answer 1

设f(x)=ax+b,则f(f(x))=f(ax+b)=a(ax+b)+b=a^2x+ab+b=16x-25,则a^2=16,ab+b=-25 ∴a=4或a=-4,①当a=4时,4b+b=-25,则b=-5,此时f(x)=4x-5 ②当a=-4时,-4b+b=-25,则b=25/3,此时f(x)=-4x+25/3