y=(ax+b)/(cx+d)的值域是{y|y≠-2}时,一定要a/c≠b/d吗?为什么?
问题描述:
y=(ax+b)/(cx+d)的值域是{y|y≠-2}时,一定要a/c≠b/d吗?为什么?
答
y=a/c+[(ax+b)-a/c*(cx+d)]/(cx+d)
=a/c+(ax+b-ax-ad/c)/(cx+d)
=a/c+(b-ad/c)/(cx+d)
∵y≠-2
∴a/c=-2,且b-ad/c≠0
∴a/c=-2且a/c≠b/d