函数y=根号5+2x-x²的值域是

函数y=根号5+2x-x²的值域是
函数y=根号5+2x-x²的值域是

函数y=根号5+2x-x²的值域是
5+2x-x²
=-x²+2x-1+6
=-(x-1)²+6≤6
根号下则0≤5+2x-x²≤6
0≤y≤√6
所以值域[0,√6]

y=√(5+2x-x²)=√[6-(x-1)²]
因为0≤6-(x-1)²≤6
所以0≤√[6-(x-1)²]≤√6
所以值域是[0,√6]

y=-(x-1)^2+根号5+1
所以值域是(-无穷，根号5+1]