假设你已经学习过指数函数的基本性质和反函数的概念,但还没有学习过对数的相关概念.由指数函数f(x)=a
x(a>0且a≠1)在实数集R上是单调函数,可知指数函数f(x)=a
x(a>0且a≠1)存在反函数y=f
-1(x),x∈(0,+∞).请你依据上述假设和已知,在不涉及对数的定义和表达形式的前提下,证明下列命题:
(1)对于任意的正实数x
1,x
2,都有f
-1(x
1x
2)=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123844044522356/SYS201310251238440445223015_ST/0.png)
;
(2)函数y=f
-1(x)是单调函数.
考点分析:
相关试题推荐
如图,某农业研究所要在一个矩形试验田ABCD内种植三种农作物,三种农作物分别种植在并排排列的三个形状相同、大小相等的矩形中.试验田四周和三个种植区域之间设有1米宽的非种植区.已知种植区的占地面积为800平方米,问:应怎样设计试验田ABCD的长与宽,才能使其占地面积最小?最小占地面积是多少?
查看答案
已知函数f(x)=cosx(sinx+cosx),x∈R.
(1)请指出函数f(x)的奇偶性,并给予证明;
(2)当
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123844044522356/SYS201310251238440445223013_ST/0.png)
时,求f(x)的取值范围.
查看答案
以下四个命题中,真命题的个数为( )
①集合{a
1,a
2,a
3,a
4}的真子集的个数为15;
②平面内两条直线的夹角等于它们的方向向量的夹角;
③设z
1,z
2∈C,若
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123844044522356/SYS201310251238440445223012_ST/0.png)
,则z
1=0且z
2=0;
④设无穷数列{a
n}的前n项和为S
n,若{S
n}是等差数列,则{a
n}一定是常数列.
A.0
B.1
C.2
D.3
查看答案
已知向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123844044522356/SYS201310251238440445223011_ST/0.png)
,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123844044522356/SYS201310251238440445223011_ST/1.png)
满足:
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123844044522356/SYS201310251238440445223011_ST/2.png)
,且
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123844044522356/SYS201310251238440445223011_ST/3.png)
(k>0).则向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123844044522356/SYS201310251238440445223011_ST/4.png)
与向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123844044522356/SYS201310251238440445223011_ST/5.png)
的夹角的最大值为( )
A.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123844044522356/SYS201310251238440445223011_ST/6.png)
B.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123844044522356/SYS201310251238440445223011_ST/7.png)
C.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123844044522356/SYS201310251238440445223011_ST/8.png)
D.
查看答案
曲线x
2+y
2-6x=0(y>0)与直线y=k(x+2)有公共点的充要条件是( )
A.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123844044522356/SYS201310251238440445223010_ST/0.png)
B.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123844044522356/SYS201310251238440445223010_ST/1.png)
C.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123844044522356/SYS201310251238440445223010_ST/2.png)
D.
查看答案