求下列函数的值域:(1)Y=(5X-1)/(4X+2);(2)Y=(X²-4x+3)/(2X²-X-1)

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/23 18:27:27
求下列函数的值域:(1)Y=(5X-1)/(4X+2);(2)Y=(X²-4x+3)/(2X²-X-1)求下列函数的值域:(1)Y=(5X-1)/(4X+2);(2)Y=(X

求下列函数的值域:(1)Y=(5X-1)/(4X+2);(2)Y=(X²-4x+3)/(2X²-X-1)
求下列函数的值域:(1)Y=(5X-1)/(4X+2);(2)Y=(X²-4x+3)/(2X²-X-1)

求下列函数的值域:(1)Y=(5X-1)/(4X+2);(2)Y=(X²-4x+3)/(2X²-X-1)
(1)
Y=(5X-1)/(4X+2)
= 5/4(X-1/5)/(X+1/2)
= 5/4(X+1/2-7/10)/(X+1/2)
= 5/4 - (7/8)/(X+1/2)
- (7/8)/(X+1/2)≠0
5/4 - (7/8)/(X+1/2)≠5/4
值域(-∞,5/4),(5/4,+∞)
(2)
Y=(X²-4x+3)/(2X²-X-1)
= (X-1)(X-3)/[(2X+1)(X-1)]
= (X-3)/(2X+1)
=1/2(2X+1-7)/(2X+1)
= 1/2 - (7/2)/(2X+1)
- (7/2)/(2X+1)≠0
1/2 - (7/2)/(2X+1)≠1/2
值域:(-∞,1/2),(1/2,+∞)