对于任意的x1,x2∈R.若函数f(x)=2^x,试比较[f(x1)+f(x2)]/2与f[(x1+x 2)/2]的大小
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/18 18:39:51
对于任意的x1,x2∈R.若函数f(x)=2^x,试比较[f(x1)+f(x2)]/2与f[(x1+x 2)/2]的大小
底数2>1,2^x恒>0
[f(x1)+f(x2)]/2/f[(x1+x2)/2]
=[(2^x1+2^x2)/2]/2^[(x1+x2)/2]
=[2^(x1-1)+2^(x2-1)]/2^[(x1+x2)/2]
=2^[x1-1 -(x1+x2)/2] +2^[x2-1-(x1+x2)/2]
=2^[(x1-x2)/2 -1]+2^[(x2-x1)/2 -1]
=(1/2)[2^[(x1-x2)/2] +1/2^[(x1-x2)]/2]
由均值不等式得2^[(x1-x2)/2]+1/2^[(x1-x2)/2]≥2,当且仅当x1=x2时取等号.
(1/2)[2^[(x1-x2)/2] +1/2^[(x1-x2)]/2]≥1
[f(x1)+f(x2)]/2≥f[(x1+x2)/2],当且仅当x1=x2时取等号
[f(x1)+f(x2)]/2/f[(x1+x2)/2]
=[(2^x1+2^x2)/2]/2^[(x1+x2)/2]
=[2^(x1-1)+2^(x2-1)]/2^[(x1+x2)/2]
=2^[x1-1 -(x1+x2)/2] +2^[x2-1-(x1+x2)/2]
=2^[(x1-x2)/2 -1]+2^[(x2-x1)/2 -1]
=(1/2)[2^[(x1-x2)/2] +1/2^[(x1-x2)]/2]
由均值不等式得2^[(x1-x2)/2]+1/2^[(x1-x2)/2]≥2,当且仅当x1=x2时取等号.
(1/2)[2^[(x1-x2)/2] +1/2^[(x1-x2)]/2]≥1
[f(x1)+f(x2)]/2≥f[(x1+x2)/2],当且仅当x1=x2时取等号
对任意x1,x2属于R,若函数f(x)=2^x,试判断 f(x1)+f(x2)/2与f[(x1+x2)/2]的大小关系?
函数f(x),x∈R,若对于任意实数x1,x2都有f(x1+x2)+f(x1-x2)=2f(x1).f(x2),求证f(
函数f(x),x属于R,若对于任意实数x1,x2,都有f(x1+x2)+f(x1-x2)=2f(x1)*f(x2),求证
对数函数题2对任意的x1,x2∈(0,+∞),若函数f(x)=lgx,试比较[f(x1)+f(x2)]/2与[f(x1+
设函数F(X)的定义域为R,对任意实数X1,X2,有F(X1)+F(X2)=2F(X1+X2/2)乘以F(X1-X2)/
设函数f(x)的定义域为R,对任意实数x1,x2,有f(x1)+f(x2)=2f{(x1+x2)/2}×f{(x1-x2
对于函数f(x)的定义域中任意的x1,x2(x1≠x2),有如下结论(1)f(x1+x2)=f(x1)*f(x2) (2
对于任意的x1,x2∈(0,+∞).若函数f(x)=lgx,试比较[f(x1)+f(x2)]/2与f[(x1+x 2)/
对于任意的x1,x2属于(0,正无穷大),若函数f(x) = lgx,试比较( f(x1)+f(x2) ) / 2 于f
已知函数f(x),x∈R,若对于任意实数x1,x2都有f(x1+x2)+f(x1-x2)=2f(x1)f(x2),试判断
已知函数f(x)=lgx(x属于R+)若x1,x2属于R+,比较1/2[f(x1)+f(x2)f[(x1+x2)/2]的
若定义在[-2010,2010]上的函数f(x)满足对于任意 x1,x2,有f(x1+x2)=f(x1)+f(x2)+2