y=(3x2+3x-1)/(x2+x-1) x属于R求值域

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y=(3x2+3x-1)/(x2+x-1)x属于R求值域y=(3x2+3x-1)/(x2+x-1)x属于R求值域y=(3x2+3x-1)/(x2+x-1)x属于R求值域y=(3x²+3x-3

y=(3x2+3x-1)/(x2+x-1) x属于R求值域
y=(3x2+3x-1)/(x2+x-1) x属于R求值域

y=(3x2+3x-1)/(x2+x-1) x属于R求值域
y=(3x²+3x-3+2)/(x²+x-1)
=(3x²+3x-3)/(x²+x-1)+2/(x²+x-1)
=3+2/(x²+x-1)
x²+x-1=(x+1/2)²-5/4>=-5/4
所以1/(x²+x-1)0
2/(x²+x-1)0
3+2/(x²+x-1)3
所以值域(-∞,7/5]∪(3,+∞)

判别式法
y=(3X^2+3X-1)/(X^2+X-1)
将分母乘过来
(y-3)X^2+(y-3)X-(y-1)=0
若使X有定义
则德塔=(y-3)^2+4(y-3)(y-1)>=0
得(y-3)(5y-7)>=0
即y€(-无穷,7/5]U[3,+无穷)