因?yàn)?原函數(shù)為減函數(shù),
所以任取x1
即y1>y2
對(duì)于反函數(shù)而言有點(diǎn)(y1,x1),(y2,x2)在函數(shù)圖像上,
所以f^-1(y1)-f^-1(y2)=x1-x2<0,
因?yàn)閥1>y1,而f^-1(y1)
如何證明一個(gè)減函數(shù)的反函數(shù)也是減函數(shù)?
如何證明一個(gè)減函數(shù)的反函數(shù)也是減函數(shù)?
單調(diào)減函數(shù)y=f(x),的反函數(shù)y=f^-1(x)也是減函數(shù)?
單調(diào)減函數(shù)y=f(x),的反函數(shù)y=f^-1(x)也是減函數(shù)?
數(shù)學(xué)人氣：121 ℃時(shí)間：2020-06-04 06:01:52
優(yōu)質(zhì)解答
設(shè)原函數(shù)y=f(x)定義域?yàn)镈
因?yàn)?原函數(shù)為減函數(shù),
所以任取x1都有f(x1)-f(x2)>0,
即y1>y2
對(duì)于反函數(shù)而言有點(diǎn)(y1,x1),(y2,x2)在函數(shù)圖像上,
所以f^-1(y1)-f^-1(y2)=x1-x2<0,
因?yàn)閥1>y1,而f^-1(y1)
因?yàn)?原函數(shù)為減函數(shù),
所以任取x1
即y1>y2
對(duì)于反函數(shù)而言有點(diǎn)(y1,x1),(y2,x2)在函數(shù)圖像上,
所以f^-1(y1)-f^-1(y2)=x1-x2<0,
因?yàn)閥1>y1,而f^-1(y1)
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