y = x+√(1-x²)
1-x²≥0
定义域：-1≤x≤1
令x=cosα
则1-x²=sin²α
y = x+√(1-x²) = cosα + |sinα|
当sinαd≥0时,α的取值范围为【2kπ,2kπ+π】：y = cosα+sinα = √2(cosαsinπ/4+sinαcosπ/4) = √2sin(α+π/4),α+π/4的取值范围为【2kπ+π/4,2kπ+π+π/4】
α+π/4=2kπ+π/2时y取极大值√2,α+π/4=2kπ+π+π/4时y取极小值-1.
当sinαd≤0时,α的取值范围为【2kπ-π,2kπ】：y = cosα-sinα = √2(cosαsinπ/4-sinαcosπ/4) = -√2sin(α-π/4),α-π/4的取值范围为【2kπ-π-π/4,2kπ-π/4】
α-π/4=2kπ-π-π/4时y取极小值-12,α-π/4=2kπ-π/2时y取极大值√2.
综上,y值域【-1,√2】