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问题: x∈(0,π/3]时,f(x)=sin[2x+(π/6)]+(1/2)的值域是?

x∈(0,π/3]时,f(x)=sin[2x+(π/6)]+(1/2)的值域是?

解答:

x∈(0,π/3]时,f(x)=sin[2x+(π/6)]+(1/2)的值域是?
解:x∈(0,π/3]→2x+π/6∈(π/6,5π/6]→
sin[2x+(π/6)]∈[1/2,1]→sin[2x+(π/6)]+(1/2)∈[1,3/2]
∴f(x)=sin[2x+(π/6)]+(1/2)的值域是:[1,3/2]