函数f(x+2)为偶函数,那么f(x)的对称轴为什么
\u82e5f(x+2)\u4e3a\u5076\u51fd\u6570\uff0c\u90a3\u4e48f(x)\u7684\u5bf9\u79f0\u8f74\u662f\u4ec0\u4e48\uff1f\u4e3a\u4ec0\u4e48\uff1f\u8981\u8be6\u89e3\u4ee4g\uff08x\uff09=f\uff08x+2\uff09
\u5219g\uff08x\uff09\u4e3a\u5076\u51fd\u6570\uff0c\u6545g\uff08x\uff09=g\uff08-x\uff09\uff0c\u5373f\uff08x+2\uff09=f\uff08-x+2\uff09
\u6240\u4ee5f\uff08x\uff09\u7684\u5bf9\u79f0\u8f74\u662fx=2\u3002
\u81f3\u4e8e\u4f60\u8ffd\u95ee\u91cc\u9762\u7684\uff0c\u867d\u7136\u4f60\u662f\u4ee4t=x+2\u4e86\uff0c\u4f46f\uff08x+2\uff09\u4e3a\u5076\u51fd\u6570\uff0c\u662f\u4ee5x\u4e3a\u81ea\u53d8\u91cf\uff0c\u800c\u4e0d\u662ft\u4e3a\u81ea\u53d8\u91cf\uff0c\u6240\u4ee5f\uff08t\uff09\u5e76\u4e0d\u7b49\u4e8ef\uff08-t\uff09\uff0c\u4e5f\u5373f\uff08t\uff09\u7684\u5bf9\u79f0\u8f74\u5e76\u4e0d\u662ft=0\uff0c\u800c\u662fx=0\u65f6t\u7684\u53d6\u503c\uff0c\u6b64\u65f6t=0+2=2\uff0c\u4e5f\u5373f\uff08t\uff09\u7684\u5bf9\u79f0\u8f74\u4e3at=2\u3002
\u51fd\u6570\u4e2d\uff0c\u56e0\u4e3a\u81ea\u53d8\u91cft\u548cx\u7684\u53d6\u503c\u8303\u56f4\u662f\u4e00\u81f4\u7684\uff0c\u5373\u5bf9\u51fd\u6570f\uff08t\uff09\u4e0ef\uff08x\uff09\u800c\u8a00\u5b9a\u4e49\u57df\u4e00\u81f4\uff0c\u5bf9\u5e94\u6cd5\u5219\u4e00\u81f4\uff0c\u6240\u4ee5\u8fd9\u4e24\u4e2a\u662f\u540c\u4e00\u4e2a\u51fd\u6570\u3002\u5c06t\u7528x\u66ff\u6362\uff0c\u5219\u53ef\u5f97\u5230f\uff08x\uff09\u7684\u5bf9\u79f0\u8f74\u662fx=2\u3002
\u5076\u51fd\u6570\u5fc5\u987b\u5173\u4e8ey\u8f74\u5bf9\u79f0\u5373x=0\uff0c\u90a3\u4e48\u7531f(x+2)\u2013>f(x)\u9700\u8981\u5411\u53f3\u5e73\u79fb\u4e24\u4e2a\u5355\u4f4d\uff0c\u53ef\u4ee5\u770b\u6210\u5bf9\u79f0\u8f74x=0\u5411\u53f3\u5e73\u79fb\u4e24\u4e2a\u5355\u4f4d\u5373x=2
f(x+2)为偶函数，说明f(x+2)=f(-x+2)即f(2+x)=f(2-x)
所以f(x)的对称轴应为x=2
选C
f(x+2)为偶函数
所以f(x+2)的对称轴是x=0
f(x+2)就是把f(x)向左移2个单位
所以f(x)是把f(x+2)向右移2个单位
所以f(x)的对称轴就是把x=0向右移2个单位,即x=2
选C
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