Question

函数y=(log1/4x)^2-log（1/4）（x^2）+5在2≤x≤4上值域为？（麻烦一下解答者详细写出过程，谢谢了）

Answer 1

解：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≤-3/2
9/4≤(log1/4 x-1)^2≤4
25/4≤(log1/4 x-1)^2+4≤8
即值域为{y|25/4≤y≤8}