y=log4(3x+1)+1/2log4(x+1),x∈【0,1】的值域

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y=log4(3x+1)+1/2log4(x+1),x∈【0,1】的值域
y=log4(3x+1)+1/2log4(x+1),x∈【0,1】的值域

y=log4(3x+1)+1/2log4(x+1),x∈【0,1】的值域

y=log4(3x+1)+0.5log2(x+1).    x∈[0,1]   求值域.

y=log4(3x+1)+0.5log2(x+1)

=0.5log2(3x+1)+0.5log2(x+1)

=0.5log2  [3(x+2/3)^2-1/3].    

x∈[0,1]时 ,函数g(x)=3(x+2/3)^2-1/3值域为{g|1≤g≤8}

所以0.5log2(1)≤y≤0.5log2 (8)即0≤y≤3/2