对于函数y=(1/2)^x²-6x+15.(1)求函数的定义域,值域.(2)确定函数的单调区间.
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对于函数y=(1/2)^x²-6x+15.(1)求函数的定义域,值域.(2)确定函数的单调区间.
对于函数y=(1/2)^x²-6x+15.(1)求函数的定义域,值域.(2)确定函数的单调区间.
对于函数y=(1/2)^x²-6x+15.(1)求函数的定义域,值域.(2)确定函数的单调区间.
函数y=(1/2)^(x²-6x+15)的定义域 x∈R
x²-6x+15=(X-3)²+6≥6 ∴y=(1/2)^(x²-6x+15)≤(1/2)^6=1/64
∴函数y=(1/2)^x²-6x+15值域 y∈(-∞,1/64]
∵x≤3时,f(x)=x²-6x+15单调递减,y=(1/2)^x单调递减
∴x≤3时,y=(1/2)^(x²-6x+15)单调递增
∵x>3时,f(x)=x²-6x+15单调递增,y=(1/2)^x单调递减
∴x>3时,y=(1/2)^(x²-6x+15)单调递减