设函数y=fx是定义在R上的奇函数，当x>0时，fx=x^-2x+3,试求y=fx在R上的解析式
\u5df2\u77e5\u51fd\u6570y=fx\u662f\u5b9a\u4e49\u5728R\u4e0a\u7684\u5947\u51fd\u6570\uff0c\uff0c\u5f53x>0\u65f6\uff0cfx=x^2-2x,\u6c42x<0,fx\u7684\u8868\u8fbe\u5f0f\u4f60\u597d\uff0c\u8fd9\u91cc\u6211\u7ed9\u4f60\u6307\u5bfc\u4e0b\uff0c\u9996\u5148\u662f\u4f60\u5bf9\u51fd\u6570\u7684\u5b9a\u4e49\u4e0d\u591f\u4e86\u89e3\u3002
\u5bf9\u4e8ey=f\uff08x\uff09\uff0c\u8fd9\u91cc\u7684x\u8868\u793a\u7684\u662f\u4e00\u4e2a\u81ea\u53d8\u91cf\uff0cy\u4e5f\u662f\u4e2a\u968f\u7740x\u53d8\u5316\u800c\u53d8\u5316\u7684\u81ea\u53d8\u91cf\u3002
y=f\uff08x\uff09\u7684\u81ea\u53d8\u91cf\u5c31\u662fx\uff0cy=f\uff08-x\uff09\u7684\u81ea\u53d8\u91cf\u5c31\u662f-x\uff0c\u82e5y=f(\u221ax)\uff0c\u90a3\u4e48\u81ea\u53d8\u91cf\u5c31\u662f\u221ax\uff0c\u6240\u4ee5\u4e0d\u80fd\u6df7\u5728\u4e00\u8d77\u4e86\u3002
\u6709\u95ee\u9898\u76f4\u63a5\u95ee\u6211
\u5df2\u77e5\u51fd\u6570y=fx\u662f\u5b9a\u4e49\u5728R\u4e0a\u7684\u5947\u51fd\u6570\uff0c\uff0c\u5f53x>=0\u65f6\uff0cfx=x^2-2x,\u6c42x<0,fx\u7684\u8868\u8fbe\u5f0f
\u89e3\uff1a
x0, f(-x)=(-x)²-2*(-x)=x²+2x
\u2235 \u662f\u5947\u51fd\u6570
\u2234 f(x)=-f(-x)=-x²-2x
f(-0)=-f(0)
f(0)=0
x<0
-x>0
f(-x)=(-x)^2+2x+3=x^2+2x+3=-f(x)
∴分段函数
f(x)=①x^2-2x+3(x>0)
②0(x=0)
③-x^2-2x-3(x<0)
函数y=fx是定义在r上的奇函数,
所以f(-x)=-f(x),
当
x>=0时,f(x)=x^2-2x-3,
令x<0,
则-x>0,
f(-x)=(-x)^2+2x-3,
=x^2+2x-3,
-f(x)=x^2+2x-3,
所以f(x)=-x^2
-2x
+3,
所以当
x>=0时,f(x)=x^2-2x-3,
当x<0时，
f(x)=-x^2
-2x
+3,
满意记得采纳，谢谢
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