已知fx是奇函数，且当x>0时，fx=x|x-2|，求x<0时，fx的解析式 已知f(x)是奇函数，且当x＞0时，f(x)=x|x-2|,...
\u5df2\u77e5f(x)\u662f\u5947\u51fd\u6570\uff0c\u4e14\u5f53x<0\u65f6\uff0cf(x)=x^2-x,\u5219\u5f53x>0\u65f6\uff0cf(x)\u7684\u89e3\u6790\u5f0f\u4e3a\u5f53x>0\u65f6\uff0c\u5219-x<0\uff0c
\u56e0\u4e3a\u5f53x<0\u65f6\uff0cf\uff08x\uff09=x^2-x\uff0c
\u6240\u4ee5f\uff08-x\uff09=\uff08-x\uff09^2-\uff08-x\uff09=x^2+x
\u53c8\u2235\u51fd\u6570f\uff08x\uff09\u662f\u5b9a\u4e49\u5728R\u4e0a\u7684\u5947\u51fd\u6570\uff0c\u5373f\uff08-x\uff09=f\uff08x\uff09\uff0c
\u2234f\uff08x\uff09=-x^2-x\uff0e
\u2234\u5f53x>0\u65f6\uff0cf\uff08x\uff09=-x^2-x\uff0e
\u671b\u91c7\u7eb3\uff0c\u8c22\u8c22
x<0,-x>0
所以f(-x)=-x|-x-2|=-x|x+2|
奇函数则f(x)=-f(-x)=x|x+2|
且f(0)=0，符合这个式子
所以f(x)=
x|x+2|，x≤0
x|x-2|。x>0
x>0时fx=x|x-2|， 可以写为f(t) = t |t-2|
奇函数，f(x)=-f(-x)
x<0, -x>0, 令 -x = t ，
f(x) = -f(-x) = - f(t) = - t |t-2|
将 t = -x，反带回上式得
f(x) = x | -x -2| = x |x+2|
希望能够帮到你
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