设函数f(x)=x^2-x+b,且满足f(log2(a)=b,log2[f(a)]=2(a>0,a不等于1) 求f(log2(x)的最小值及对应的x值

问题描述:

设函数f(x)=x^2-x+b,且满足f(log2(a)=b,log2[f(a)]=2(a>0,a不等于1) 求f(log2(x)的最小值及对应的x值
若f(log2 x)>f(1),且log2f(x)<f(1),求x的取值范围

1.f(x)=x^2-x+b,且f[log2(a)]=b
所以log2 a)^2-log2 a +b=b
log2a(log2a-1)=0,a≠1
所以a=2
log2 [f(a)]=2,即log2 f(2)=2
log2 (2+b)=2,所以b=2
f(log2 x)=(log2 x)^2-log2 x+2
=(log2 x-0.5)^2+7/4
当log2 x=0.5,x=√2时,f(log2 x)取最小值7/4
2.f(log2 x)>f(1)
即(log2 x)^2-log2 x+2>2
log2 x>2 或log2 x2或0(log2 x)^2-log2 x+2>2 log2 x>2 或log2 x1 或log2 x2或0