求y=(ax+b)÷(cx+d)(ac≠0,ad≠bc)的值域,请问是如何得到﹛y|y≠a/c﹜

Question

求y=(ax+b)÷(cx+d) (ac≠0,ad≠bc)的值域,请问是如何得到﹛y|y≠a/c﹜

Answer 1

解y=(ax+b)÷(cx+d)
=(a/c(cx+d）+b-ad/c)÷(cx+d)
=(a/c(cx+d）+bc/c-ad/c)÷(cx+d)
=(a/c(cx+d）+(bc-ad)/c)÷(cx+d)
=a/c+[(bc-ad)/c]÷(cx+d)
由ad≠bc知(bc-ad)/c≠0
即[(bc-ad)/c]÷(cx+d) ≠0
即a/c+[(bc-ad)/c]÷(cx+d) ≠a/c
即y≠a/c
故函数的值域为｛y/y≠a/c｝