求函数y=根号下1+x加根号下1-x的值域

Question

如题所述

Answer 1

y=√(1+x) +√(1-x)
1+x≥0 and 1-x≥0
x≥-1 and x≤1
-1≤x≤1

y=√(1+x) +√(1-x)
y' = 1/[2√(1+x) ] - 1/[2√(1-x) ]

y'=0
√(1-x) = √(1+x)
x=0

y'(0+) <0
y'(0-) >0
x=0 (max)

y(0) =2
y(-1) = √2
y(1) = √2

值域 =[√2 ,2]