设函数f(x)与g(x)分别满足f(x+1/2)=log1/2 (x²-9/4)和g(x)=log1/2 (x-1)-1(1)求函数f(x)的表达式;(2)若f(x)>g(x),求x的取值范围.
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设函数f(x)与g(x)分别满足f(x+1/2)=log1/2 (x²-9/4)和g(x)=log1/2 (x-1)-1(1)求函数f(x)的表达式;(2)若f(x)>g(x),求x的取值范围.
设函数f(x)与g(x)分别满足f(x+1/2)=log1/2 (x²-9/4)和g(x)=log1/2 (x-1)-1
(1)求函数f(x)的表达式;
(2)若f(x)>g(x),求x的取值范围.
设函数f(x)与g(x)分别满足f(x+1/2)=log1/2 (x²-9/4)和g(x)=log1/2 (x-1)-1(1)求函数f(x)的表达式;(2)若f(x)>g(x),求x的取值范围.
(1) 令t=x+1/2,则x=t-1/2 f(t)=log1/2[(t-1/2)^2-9/4]=log1/2(t^2-t-2)
故 f(x)=log1/2(x^2-x-2)
(2) f(x)=log1/2(x^2-x-2)>g(x)=log1/2(x-1)-1=log1/2(x-1)-log1/2(1/2)=log1/2(2x-2) (1)
1/20; 2x-2>0; x^2-x-2
(1)
f(x)=log1/2 ((x-1/2)²-9/4)
=log1/2 (x²-x/2-2)
(2)
g(x)=(log1/2 (x-1))-1
=log1/2 (x-1)/(1/2)
=log1/2 2(x-1)
f(x)>g(x)即
log1/2 (x²-x/2-2)>log1/2 2(...
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(1)
f(x)=log1/2 ((x-1/2)²-9/4)
=log1/2 (x²-x/2-2)
(2)
g(x)=(log1/2 (x-1))-1
=log1/2 (x-1)/(1/2)
=log1/2 2(x-1)
f(x)>g(x)即
log1/2 (x²-x/2-2)>log1/2 2(x-1)
因为1/2<1,所以等于求
(x²-x/2-2)<2(x-1)
x²-x/2-2-2x+2<0
x²-5x/2<0
所以x的取值范围是0
收起
f(x)=log1/2 (x²-x/4-2)
0
F[GX]