函数定义域为[-√5,√5]
令x=√5cosα,α∈[0,π]
则y=√5cosα+|√5sinα|
=√5cosα+√5sinα
=√10sin(α+π/4)
∵α∈[0,π]
∴α+π/4∈[π/4,5π/4]
sin(α+π/4) ∈[-√2/2,1 ]
∴函数的值域为[-√5,√10 ].