已知函数f(x)满足f(x+1/2)=log1/2(x^2-9/4),函数g(x)=log1/2(x-1)求：函数f(x)的表达式；若f(x)>g(x),求x的取值范围.

已知函数f(x)满足f(x+1/2)=log1/2(x^2-9/4),函数g(x)=log1/2(x-1)求：函数f(x)的表达式；若f(x)>g(x),求x的取值范围.
已知函数f(x)满足f(x+1/2)=log1/2(x^2-9/4),函数g(x)=log1/2(x-1)
求：函数f(x)的表达式；
若f(x)>g(x),求x的取值范围.

已知函数f(x)满足f(x+1/2)=log1/2(x^2-9/4),函数g(x)=log1/2(x-1)求：函数f(x)的表达式；若f(x)>g(x),求x的取值范围.
令a=x+1/2
x^2=(a-1/2)^2=a^2-a+1/4
x^2-9/4=a^2-a-2
所以f(a)=log1/2(a^2-a-2)
f(x)=log1/2(x^2-x-2)
f(x)>g(x)
定义域
x^2-x-2>0
(x-2)(x+1)>0
x>2,x0
x>1
所以x>2
底数=1/2

f(x+1/2)=log1/2(x^2-9/4),
令x+1/2=t
x=t-1/2
f(t)=log1/2((t-1/2)^2-9/4)
=log1/2(t^2-t-2)
所以
f(x)=log1/2(x^2-x-2)
(2)
f(x)>g(x)
log1/2(x^2-x-2)>log1/2(x-1)

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f(x+1/2)=log1/2(x^2-9/4),
令x+1/2=t
x=t-1/2
f(t)=log1/2((t-1/2)^2-9/4)
=log1/2(t^2-t-2)
所以
f(x)=log1/2(x^2-x-2)
(2)
f(x)>g(x)
log1/2(x^2-x-2)>log1/2(x-1)
y=log1/2x是减函数,
所以
x^2-x-2x^2-2x-1<0
1-√2又
x^2-x-2>0
(x+1)(x-2)>0
x<-1,x>2
x-1>0
x>1
取交集,有:
2

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