已知函数f loga（x）=（1/2x次方-1+...

来源：蜘蛛抓取(WebSpider) 时间：2011-10-23 10:40 标签： 已知函数f loga
已知定义在r上的函数f(x)等于2x次方+1分之a-2x次方是奇函数 求实数a的值 判断f(x)的单调性,并证明
f(x)=(a-2^x)/(2^x+1)
跪求帮解出来
f(x)是奇函数, 所以f(-x)=-f(x)
即 (a-2^(-x))/(2^(-x)x+1)=-(a-2^x)/(2^x+1)
a*2^x-1=2^x-a
(a-1)2^x=1-a
因上式对任何x都成立, 所以 a-1=0,
f(x)=(1-2^x)/(1+2^x)
f'(x)=((1-2^x)'(1+2^x)-(1-2^x)(1+2^x)')/(1+2^x)²
=(-2^xln2(1+2^x)-(1-2^x)(2^xln2))/(1+2^x)²
=2^xln2(2^x-1-1-2^x)/(1+2^x)²
=-2ln2*2^x/(1+2^x)²
因此, f'(x)<0
f(x) 单调递减
为您推荐：
其他类似问题
扫描下载二维码The page is temporarily unavailable
nginx error!
The page you are looking for is temporarily unavailable.
Please try again later.
Website Administrator
Something has triggered an error on your
This is the default error page for
nginx that is distributed with
It is located
/usr/share/nginx/html/50x.html
You should customize this error page for your own
site or edit the error_page directive in
the nginx configuration file
/etc/nginx/nginx.conf.The page is temporarily unavailable
nginx error!
The page you are looking for is temporarily unavailable.
Please try again later.
Website Administrator
Something has triggered an error on your
This is the default error page for
nginx that is distributed with
It is located
/usr/share/nginx/html/50x.html
You should customize this error page for your own
site or edit the error_page directive in
the nginx configuration file
/etc/nginx/nginx.conf.已知函数F（x）=A的2x次方+2乘以A的x次方再减一在闭区间-1到1上的最大值为14,求实数A的取值.
暗袭低调175
由题目,得到:F(x)=A^(2X)+2A^x-1=(A^x+1)^2-2-----------(1)设y(x)=A^x,-----------(2)则有:F(x)=(y(x)+1)^2-2,所以有:F(y)=(y+1)^2-2----------------(3)由于(2)式函数y(x)是单调函数,1.如果A>1,则为递增函数,y在[-1,1]上的值为:[A^(-1),A]而(3)式函数F(y)在[A^(-1),A]区间上也是单调上升的,所以,最大值为y=A时的值,即:F(A)=(A+1)^2-2,由题目已知为14,所以:(A+1)^2-2=14,即:A=32.如果A
为您推荐：
其他类似问题
扫描下载二维码已知函数f(x)=2x次方+2-x次方分之2x次方-2-x次方(1)求f(x)的定义域与值域_百度知道

我要回帖

更多关于 已知函数f loga 的文章

 

随机推荐