函数y=(1/2)^x方-6x的定义域,值域并确定函数的单调区间
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2014-12-07 · 知道合伙人教育行家
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y = (1/2)^(x^2-6x)
定义域:x属于R
x^2-6x = (x-3)²-9 ≥ -9
(1/2)^(-9)=2^9 = 512
0 < (1/2)^(x^2-6x) ≤ 512
值域:(0,512]
x<3时,(x^2-6x)单调减,(1/2)^(x^2-6x)单调增;x>3时,(x^2-6x)单调增减,(1/2)^(x^2-6x)单调减,故:
单调增区域:(-无穷大,3);单调减区间(3,+无穷大)
定义域:x属于R
x^2-6x = (x-3)²-9 ≥ -9
(1/2)^(-9)=2^9 = 512
0 < (1/2)^(x^2-6x) ≤ 512
值域:(0,512]
x<3时,(x^2-6x)单调减,(1/2)^(x^2-6x)单调增;x>3时,(x^2-6x)单调增减,(1/2)^(x^2-6x)单调减,故:
单调增区域:(-无穷大,3);单调减区间(3,+无穷大)
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