函数y=(x^2-4x-5)/(x^2-3x-4)的值域是?..

题目

函数y=(x^2-4x-5)/(x^2-3x-4)的值域是?..

答案

∵y=(x²-4x-5)/(x²-3x-4)=(x-5)(x+1)/(x-4)(x+1)=(x-5)/(x-4)=1-1/(x-4)∴原函数与函数y=1-1/(x-4) (x≠4且x≠-1)等同又∵函数y=1-1/(x-4) (x≠4)的值域为R∴原函数的值域为y≠6/5即{y|y≠6/5}...