函数y=√-X^2-2X+3的值域是 ? 写一下详细的过程

2025-02-26 18:31:31
推荐回答(2个)
回答1:

-x^2-2x+3>=0
x^2+2x-3<=0
(x+3)(x-1)<=0
-3<=x<=1
令t=-x^2-2x+3
=-(x^2+2x-3)
=-((x+1)^2-4)
=-(x+1)^2+4
-3<=x<=1
x=-1,tmax=4
x=-3orx=1,tmin=0
0<=t<=4
0<=y<=2
值域是[0,2]

回答2:

y=√-X^2-2X+3
=√[-(X+1)^2+4]
(X+1)^2≥0
0≤-(X+1)^2+4≤4
0 ≤y≤2