2个回答
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f(x) 是奇函数
=> f(0) =0
f(-2)= f(-2+2)= f(0) = 0
case 1: x∈(-2,-1)
=>-x+4∈(2,3)
f(-x)
=f(-x+4)
=(-x+4)^2-(-x+4) -1
=x^2-7x +11
f(x) =-f(-x)
=-(x^2-7x +11)
case 2: x∈(-1,0)
-x∈(0, 1)
-x+2∈(2, 3)
f(-x)
=f(-x+2)
=(-x+2)^2-(-x+2) -1
=x^2-3x +1
f(x) =-f(-x)
=-(x^2-3x +1)
ie
f(x)
=0 ; x=0 or -2
=-(x^2-7x +11) ; -2<x<-1
=-(x^2-3x +1) ; -1<x< 0
=> f(0) =0
f(-2)= f(-2+2)= f(0) = 0
case 1: x∈(-2,-1)
=>-x+4∈(2,3)
f(-x)
=f(-x+4)
=(-x+4)^2-(-x+4) -1
=x^2-7x +11
f(x) =-f(-x)
=-(x^2-7x +11)
case 2: x∈(-1,0)
-x∈(0, 1)
-x+2∈(2, 3)
f(-x)
=f(-x+2)
=(-x+2)^2-(-x+2) -1
=x^2-3x +1
f(x) =-f(-x)
=-(x^2-3x +1)
ie
f(x)
=0 ; x=0 or -2
=-(x^2-7x +11) ; -2<x<-1
=-(x^2-3x +1) ; -1<x< 0
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