高数 Y＝arcsinx－1/3，求定义域 详解，谢谢 y＝arcsin1－x/3的定义域

\u6c42y=arcsinx-1/2\u7684\u5b9a\u4e49\u57df

y=arcsinx-1/2\u7684\u5b9a\u4e49\u57df\uff1a[-1\uff0c1]
\u6c42\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u53ef\u4ee5\u901a\u8fc7\u6c42\u53cd\u51fd\u6570\u7684\u503c\u57df\uff1a
y=arcsinx-1/2\u7684\u53cd\u51fd\u6570\u4e3a\uff1ax=sin\uff08y+1/2\uff09\uff0c\u503c\u57df\u4e3a[-1\uff0c1]\u3002
\u5373y=arcsinx-1/2\u7684\u5b9a\u4e49\u57df\uff1a[-1\uff0c1]\u3002
\u8bbeD\u3001M\u4e3a\u4e24\u4e2a\u975e\u7a7a\u5b9e\u6570\u96c6\uff0c\u5982\u679c\u6309\u7167\u67d0\u4e2a\u786e\u5b9a\u7684\u5bf9\u5e94\u6cd5\u5219f\uff0c\u4f7f\u5f97\u5bf9\u4e8e\u96c6\u5408D\u4e2d\u7684\u4efb\u610f\u4e00\u4e2a\u6570x\uff0c\u5728\u96c6\u5408M\u4e2d\u90fd\u6709\u552f\u4e00\u786e\u5b9a\u7684\u6570y\u4e0e\u4e4b\u5bf9\u5e94\uff0c\u90a3\u4e48\u5c31\u79f0f\u4e3a\u5b9a\u4e49\u5728\u96c6\u5408D\u4e0a\u7684\u4e00\u4e2a\u51fd\u6570\uff0c\u8bb0\u505ay=f(x)\u3002
\u5176\u4e2d\uff0cx\u4e3a\u81ea\u53d8\u91cf\uff0cy\u4e3a\u56e0\u53d8\u91cf\uff0cf\u79f0\u4e3a\u5bf9\u5e94\u5173\u7cfb\uff0c\u96c6\u5408D\u6210\u4e3a\u51fd\u6570f(x)\u7684\u5b9a\u4e49\u57df\uff0c\u4e3a\u51fd\u6570f\u7684\u503c\u57df\uff0c\u5bf9\u5e94\u5173\u7cfb\u3001\u5b9a\u4e49\u57df\u3001\u503c\u57df\u4e3a\u51fd\u6570\u7684\u4e09\u8981\u7d20\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u6c42\u5b9a\u4e49\u57df\u7684\u4f9d\u636e
1\u3001\u5206\u5f0f\u7684\u5206\u6bcd\u4e0d\u80fd\u4e3a\u96f6\u3002
2\u3001\u5076\u6b21\u65b9\u6839\u7684\u88ab\u5f00\u65b9\u6570\u4e0d\u5c0f\u4e8e\u96f6\u3002
3\u3001\u5bf9\u6570\u51fd\u6570\u7684\u771f\u6570\u5fc5\u987b\u5927\u4e8e\u96f6\u3002
4\u3001\u6307\u6570\u51fd\u6570\u548c\u5bf9\u6570\u51fd\u6570\u7684\u5e95\u6570\u5fc5\u987b\u5927\u4e8e\u96f6\u4e14\u4e0d\u7b49\u4e8e1\u3002

y\uff1darcsin1\uff0dx/3\u7684\u5b9a\u4e49\u57df\u662f\u5168\u4f53\u5b9e\u6570\u3002
y\uff1darcsin(1\uff0dx/3)\u7684\u5b9a\u4e49\u57df\u662f[0\uff0c6]
\u56e0\u4e3a -1\u22641-x/3\u22641
-2\u2264-x/3\u22640
-6\u2264-x\u22640
0\u2264x\u22646
\u6240\u4ee5 \u5b9a\u4e49\u57df\u662f[0\uff0c6]

求函数y=arcsin[(x-1)/3]的定义域
解：由-1≦(x-1)/3≦1得 -3≦x-1≦3；∴-2≦x≦4;即该函数的定义域为[-2，4];

反正弦的定义域为-1到1

全体实数R

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