函数f(x)=log2^(x+1)+alog2^(1-x)是奇函数,a属于R(1)求a的值(2)判断并证明函数f(x)在定义域上的单调性(3)若mm
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![函数f(x)=log2^(x+1)+alog2^(1-x)是奇函数,a属于R(1)求a的值(2)判断并证明函数f(x)在定义域上的单调性(3)若mm](/uploads/image/z/7838999-71-9.jpg?t=%E5%87%BD%E6%95%B0f%28x%29%3Dlog2%5E%28x%2B1%29%2Balog2%5E%281-x%29%E6%98%AF%E5%A5%87%E5%87%BD%E6%95%B0%2Ca%E5%B1%9E%E4%BA%8ER%EF%BC%881%EF%BC%89%E6%B1%82a%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89%E5%88%A4%E6%96%AD%E5%B9%B6%E8%AF%81%E6%98%8E%E5%87%BD%E6%95%B0f%28x%29%E5%9C%A8%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%8A%E7%9A%84%E5%8D%95%E8%B0%83%E6%80%A7%EF%BC%883%EF%BC%89%E8%8B%A5mm)
函数f(x)=log2^(x+1)+alog2^(1-x)是奇函数,a属于R(1)求a的值(2)判断并证明函数f(x)在定义域上的单调性(3)若mm
函数f(x)=log2^(x+1)+alog2^(1-x)是奇函数,a属于R
(1)求a的值
(2)判断并证明函数f(x)在定义域上的单调性
(3)若mm
函数f(x)=log2^(x+1)+alog2^(1-x)是奇函数,a属于R(1)求a的值(2)判断并证明函数f(x)在定义域上的单调性(3)若mm
(1)f(x)=log2^(x+1)+alog2^(1-x)是奇函数,f(-x)=- f(x)
log2^(1+(-x))+alog2^(1-(-x))=-[log2^(x+1)+alog2^(1-x)]
a[log2^(1+x)+log2^(1-x)]=-[log2^(x+1)+alog2^(1-x)]
a=-1
原函数f(x)=log2^(x+1)/(1-x)
(2)由复合函数性质得:求f(x)=log2^(x+1)/(1-x)单调 转化为求y=( x+1)/(1-x)单调 很明显为单调递增,故原函数单调递增
(3)先求出反函数,然后与m建立不等式,即2的X次幂>(1+m)/(m-1)
对m
(1)f(x)=log2^(x+1)+alog2^(1-x)是奇函数,f(-x)=- f(x)
log2^(1+(-x))+alog2^(1-(-x))=-[log2^(x+1)+alog2^(1-x)]
a[log2^(1+x)+log2^(1-x)]=-[log2^(x+1)+alog2^(1-x)]
a=-1
原函数f(x)=log2^(x+1)-log2^...
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(1)f(x)=log2^(x+1)+alog2^(1-x)是奇函数,f(-x)=- f(x)
log2^(1+(-x))+alog2^(1-(-x))=-[log2^(x+1)+alog2^(1-x)]
a[log2^(1+x)+log2^(1-x)]=-[log2^(x+1)+alog2^(1-x)]
a=-1
原函数f(x)=log2^(x+1)-log2^(1-x)
(2) f'(x)=((x+1)log2-(1-x)log2)'=(2xlog2)'=2log2>0单调递增
(3) f(x)=log2^(x+1)-log2^(1-x)=2xlog2 f^-1(x)=1/2xlog2>=1
|x|>=1/2log2
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(1)f(x)=log2^(x+1)+alog2^(1-x)是奇函数,f(-x)=- f(x)
则有log2^(1-x)+alog2^(1+x)=-[log2^(x+1)+alog2^(1-x)]
a[log2^(1+x)+log2^(1-x)]=-[log2^(x+1)+alog2^(1-x)]
则有:a=-1
则f(x)=log2^(x+1)-log2^(1-x)
(2)由1+x>=0 ,1-x>=0求出定义域-1=《x《=1。。。。单调递增。。。