f(x+2)是偶函数,则它的对称轴是多少,是x= f(x+2)是偶函数,则它的对称轴是多少,是x=-2还是x=...

\u82e5\u51fd\u6570f(x+2)\u662f\u5076\u51fd\u6570\uff0c\u90a3\u4e48\u5b83\u7684\u5bf9\u79f0\u8f74\u5e94\u8be5\u662f\u591a\u5c11

\u4e3a\u53d9\u8ff0\u65b9\u4fbf\uff0c\u628ax+2\u770b\u505a\u4e00\u4e2a\u6574\u4f53\uff0c\u53ef\u4ee5\u8bbe
x+2=t\uff0c\u5219x=t-2.
\u2235f(x+2)\u662f\u5076\u51fd\u6570\uff0c
\u2234f(t)=f(-t)\uff0c\u4e14\u56fe\u8c61\u5173\u4e8et=0\u5bf9\u79f0\uff0c
\u2234\u56fe\u8c61\u5173\u4e8ex+2=0\u5373x=-2\u5bf9\u79f0\u3002

\u4f60\u8ba4\u4e3a\u7684f(x+2)=f(-x-2),\u662f\u5bf9\u51fd\u6570\u7684\u7406\u89e3\u6709\u8bef\u3002
\u6309\u7167\u5076\u51fd\u6570\u7684\u5b9a\u4e49\uff0c\u628a\u51fd\u6570\u7684\u81ea\u53d8\u91cf\u6362\u6210\u5176\u76f8\u53cd\u6570\u51fd\u6570\u503c\u4e0d\u53d8\uff0c\u51fd\u6570\u5c31\u662f\u5076\u51fd\u6570\u3002
f(x+2)\u7684\u81ea\u53d8\u91cf\u662fx\uff0c\u800c\u4e0d\u662fx+2\uff0c
\u56e0\u6b64f(x+2)\u662f\u5076\u51fd\u6570\uff0c\u53ea\u80fd\u628ax\u6362\u4e3a-x\u5f97
f(-x+2)=f(x+2)\uff08\u539f\u51fd\u6570\uff09\uff0c\u5e76\u975ef(x+2)=f(-x-2)\u3002

\u662fx=-2.\u56e0\u4e3a\u5982\u679cf(x)\u662f\u5076\u51fd\u6570\uff0c\u5219\u5bf9\u79f0\u8f74\u662fx=0,\u90a3\u4e48f(x+2)\u662f\u5076\u51fd\u6570\uff0c\u5219\u5b83\u7684\u5bf9\u79f0\u8f74\u662fx+2=0,\u6240 \u4ee5x=-2.

f(x+2)的对称轴就是x=0
f(x)的对称轴是x=2.因为f(x)相当于f(x+2)向右平移2个单位(左加右减)

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