y=2^x+1分之2^的反函數(shù)?
y=2^x+1分之2^的反函數(shù)?
優(yōu)質(zhì)解答
你好,題不太清楚啊
y=(2^x)/(2^x +1)
y(2^x +1)=2^x
(y-1)(2^x)=-1
2^x=1/(1-y)
x=log2 (1-y) (這里2是底數(shù),1-y是真數(shù))
所以反函數(shù)是y=log2 (1-x) (0注意反函數(shù)的定義域就是原函數(shù)的值域你答案不對的,答案是y=log2 x/1-x 。2是底數(shù)。這兩步怎么變過來的y(2^x +1)=2^x(y-1)(2^x)=-1再幫我算一下好嗎?呵呵, 不好意思確實(shí)算錯了y=(2^x)/(2^x +1)將分母乘到左邊得y(2^x +1)=2^x即y(2^x)+y-2^x=0提公因式(y-1)(2^x)=-y2^x=-y/(y-1)即2^x=y/(1-y)兩邊取以2為底的對數(shù)x=log2 [y/(1-y)]x改寫成y,y改寫成x得反函數(shù)是y=log2 [x/(1-x)] (0
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