Question

已知函数f(x)满足f(2x-3)=4x平方—2x-1 (1)求f(x)的解析试 (2)设g(x)=f(x-a)-7x,

Answer 1

(1)f(2x－3)=4x²-2x-1

∴f(2x－3)=（2x-3）²+5（2x-3）+5

由于函数f(x)满足f(2x-3)=4x²—2x-1

∴f(x)＝x²+5x+5

(2)g(x)=f(x-a)-7x=（x-a）²+5（x-a）+5-7x

=x²-(2a+2)x+a²-5a+5

易知g(x)的对称轴为a+1,且开口向上

讨论：当a+1∈[1,3]时,即0≦a≦2,

g(x)min=(a+1)²-(2a+2)(a+1)+a²-5a+5

=-7a+4;(0≦a≦2)

当a+1