已知函数f(x)=根号2sin(x+π/4) 若x∈(0,π/2)时的值域

问题描述:

已知函数f(x)=根号2sin(x+π/4) 若x∈(0,π/2)时的值域

f(x)=√2sin(x+π/4)
∵x∈(0,π/2)
∴x+π/4∈(π/4,π/2)
∴sin(x+π/4) ∈(√2/2,1]
∴√2sin(x+π/4) ∈(1,√2]
即函数值域为(1,√2]