已知函数fx=log0.5(4x)·log0.5(x/8),x∈(1/2,4],求函数的值域.
1个回答

f(x) = log0.5(4x)·log0.5(x/8)

= { log0.5(4) + log0.5(x)} {log0.5(x)-log0.5(/8) }

= { -2 + log0.5(x)} {log0.5(x)+3 }

= {log0.5(x)+3 } {log0.5(x)-2 }

= {log0.5(x)}^2+ log0.5(x) - 6

= { log0.5(x)+1/2 }^2 - 25/4

x属于(1/2,4]

log0.5(x)属于[-2,1)

log0.5(x)+1/2属于[-3/2,3/2)

{ log0.5(x)+1/2 }^2属于【0,9/4)

{ log0.5(x)+1/2 }^2-25/4属于【-25/4,-4)

值域:【-25/4,-4)