f (x) =根号2sin (x +π/4),x属于【-π/4,2π/3】求值域f(x)=(根号2)sin(x +π/4)

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f (x) =根号2sin (x +π/4),x属于【-π/4,2π/3】求值域f(x)=(根号2)sin(x +π/4)
f (x) =根号2sin (x +π/4),x属于【-π/4,2π/3】求值域
f(x)=(根号2)sin(x +π/4)

f (x) =根号2sin (x +π/4),x属于【-π/4,2π/3】求值域f(x)=(根号2)sin(x +π/4)
x属于【-π/4,2π/3】
x +π/4属于【0,11π/12】
当x=-π/4时sin (x +π/4)取最小值0,2sin (x +π/4)取最小值0
当x=π/4时sin (x +π/4)取最大值1,2sin (x +π/4)取最大值2
根号2sin (x +π/4)值域是【0,根号2】