函数y=(log1/4x)^2-log(1/4)(x^2)+5在2≤x≤4上值域为?

问题描述:

函数y=(log1/4x)^2-log(1/4)(x^2)+5在2≤x≤4上值域为?

原式=(log1/4 x)^2-2*log(1/4) x+5=(log1/4 x-1)^2+4由2≤x≤4,得log1/4 4≤log1/4 x≤log1/4 2即-1≤log1/4 x≤-1/2-2≤log1/4 x-1≤-3/29/4≤(log1/4 x-1)^2≤425/4≤(log1/4 x-1)^2+4≤8即值域为{y|25/4≤y≤8}...