y=x+根号(4-x²)值域我算的[-2√2,2√2],答案是[-2,2√2]
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![y=x+根号(4-x²)值域我算的[-2√2,2√2],答案是[-2,2√2]](/uploads/image/z/8639677-37-7.jpg?t=y%3Dx%2B%E6%A0%B9%E5%8F%B7%EF%BC%884-x%26%23178%3B%EF%BC%89%E5%80%BC%E5%9F%9F%E6%88%91%E7%AE%97%E7%9A%84%5B-2%E2%88%9A2%2C2%E2%88%9A2%5D%2C%E7%AD%94%E6%A1%88%E6%98%AF%5B-2%2C2%E2%88%9A2%5D)
y=x+根号(4-x²)值域我算的[-2√2,2√2],答案是[-2,2√2]
y=x+根号(4-x²)值域
我算的[-2√2,2√2],答案是[-2,2√2]
y=x+根号(4-x²)值域我算的[-2√2,2√2],答案是[-2,2√2]
答:
y=x+√(4-x²),定义域满足:4-x²>=0,-2<=x<=2
√(4-x²)=y-x>=0,y>=x>=-2
两边平方:
4-x²=y²-2yx+x²
2x²-2yx+y²-4=0
判别式=(-2y)²-4*2*(y²-4)>=0
4y²-8y²+32>=0
y²<=8
-2√2<=y<=2√2
综上所述,-2<=y<=2√2
所以:值域为[-2,2√2]