"函数fx在数集X上有定义"是啥意思 求大神！！！！设函数f(x)在数集X上有定义，试证:函数f(...

\u6c42\u5927\u795e\uff01\uff01\u8bbe\u51fd\u6570f\uff08x\uff09\u5728\u6570\u96c6X\u4e0a\u6709\u5b9a\u4e49\uff0c\u8bd5\u8bc1:\u51fd\u6570f(x)\u5728X\u4e0a\u6709\u754c\u7684\u5145\u5206\u5fc5\u8981\u6761\u4ef6\u662f\u5728X\u4e0a\u65e2\u6709\u4e0a

\u5fc5\u8981\u6027\uff1a
\u56e0\u4e3a\uff0cf(x)\u5728X\u4e0a\u6709\u754c
\u5373\uff0c\u5b58\u5728M>0\uff0c\u5bf9\u4efb\u610fx\u2208X\uff0c\u6709|f(x)|<M
\u5219\uff0c\u5bf9\u4efb\u610fx\u2208X\uff0c -M< f(x)<M
\u6240\u4ee5\uff0cf(x)\u5728X\u4e0a\uff0c\u65e2\u6709\u4e0a\u754cM\uff0c\u53c8\u6709\u4e0b\u754c-M
\u5145\u5206\u6027\uff1a
\u56e0\u4e3a\uff0cf(x)\u5728X\u4e0a\u65e2\u6709\u4e0a\u754c\u53c8\u6709\u4e0b\u754c
\u7531\u786e\u754c\u5b9a\u7406\u77e5f(x)\u5728X\u4e0a\u65e2\u6709\u4e0a\u786e\u754cF\uff0c\u53c8\u6709\u4e0b\u786e\u754cG
\u5219\uff0c\u5bf9\u4efb\u610fx\u2208X\uff0cG-1< G\u2264f(x)\u2264F<F+1
\u4ee4\uff0cM\uff1dmax{|G-1|\uff0c|F+1|}
\u5219\uff0c\u5bf9\u4efb\u610fx\u2208X\uff0c |f(x)|<M\u6210\u7acb
\u6240\u4ee5\uff0c\u51fd\u6570f(x)\u5728X\u4e0a\u6709\u754c
\u7efc\u4e0a\u53ef\u5f97\uff1a\u51fd\u6570f(x)\u5728X\u4e0a\u6709\u754c\u7684\u5145\u5206\u5fc5\u8981\u6761\u4ef6\u662f\u5728X\u4e0a\u65e2\u6709\u4e0a\u754c\u53c8\u6709\u4e0b\u754c
\u7b80\u4ecb\uff1a
\u6709\u754c\u51fd\u6570\u662f\u8bbef(x)\u662f\u533a\u95f4E\u4e0a\u7684\u51fd\u6570\uff0c\u82e5\u5bf9\u4e8e\u4efb\u610f\u7684x\u5c5e\u4e8eE\uff0c\u5b58\u5728\u5e38\u6570m\u3001M\uff0c\u4f7f\u5f97m\u2264f(x)\u2264M\uff0c\u5219\u79f0f(x)\u662f\u533a\u95f4E\u4e0a\u7684\u6709\u754c\u51fd\u6570\u3002\u5176\u4e2dm\u79f0\u4e3af(x)\u5728\u533a\u95f4E\u4e0a\u7684\u4e0b\u754c\uff0cM\u79f0\u4e3af(x)\u5728\u533a\u95f4E\u4e0a\u7684\u4e0a\u754c\u3002
\u6709\u754c\u51fd\u6570\u5e76\u4e0d\u4e00\u5b9a\u662f\u8fde\u7eed\u7684\u3002\u6839\u636e\u5b9a\u4e49\uff0cƒ\u5728D\u4e0a\u6709\u4e0a\uff08\u4e0b\uff09\u754c\uff0c\u5219\u610f\u5473\u7740\u503c\u57dfƒ(D)\u662f\u4e00\u4e2a\u6709\u4e0a\uff08\u4e0b\uff09\u754c\u7684\u6570\u96c6\u3002\u6839\u636e\u786e\u754c\u539f\u7406\uff0cƒ\u5728\u5b9a\u4e49\u57df\u4e0a\u6709\u4e0a\uff08\u4e0b\uff09\u786e\u754c\u3002
\u4e00\u4e2a\u7279\u4f8b\u662f\u6709\u754c\u6570\u5217\uff0c\u5176\u4e2dX\u662f\u6240\u6709\u81ea\u7136\u6570\u6240\u7ec4\u6210\u7684\u96c6\u5408N\u3002\u7531ƒ (x)=sinx\u6240\u5b9a\u4e49\u7684\u51fd\u6570f:R\u2192R\u662f\u6709\u754c\u7684\u3002\u5f53x\u8d8a\u6765\u8d8a\u63a5\u8fd1-1\u62161\u65f6\uff0c\u51fd\u6570\u7684\u503c\u5c31\u53d8\u5f97\u8d8a\u6765\u8d8a\u5927\u3002

即数集X是函数fx的定义域。

数集X属于函数的定义域

扩展阅读：任意x存在x使得fxgx ... 函数y f x ... fx f x ... 存在fx大于任意gx ... x 1 ... 已知fxy求fxx ... 求函数f x x ... 函数f x x ... &quot 破坏&quot ...