求函数y=3x+2⼀2-x 定义域为x∈(2,3)的值域.

2024-12-03 21:58:25
推荐回答(3个)
回答1:

函数y=3x+2/2-x
=[(3x-6)+8]/(2-x)
=-3-8/(x-2)
y+3=-8/(x-2)
x-2=-8/(y+3)
x= x∈(2,3) x-2∈(0,1)
0<-8/(y+3)<1
-1<8/(y+3)<0
y+3<-8
y<-11
函数y=3x+2/2-x 定义域为x∈(2,3)的值域. (-无穷,-11)

回答2:

x²-3x+2=(x-3/2)²-1/4
∵0<1/3<1
∴根据复合函数,同增异减的性质可得:(-∞,3/2)上单调递增,(3/2,+∞)上单调递减;
定义域为(-∞,+∞);
∵x²-3x+2≥-1/4
∴0

回答3:

1