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考生在练习和考试的时候经常遇到这样一类函数性质考查题:例1已知函数f(x)=a~x(a>1)的定义域与值域均为[m,n](mx对任意的实数x恒成立,则实数a的取值范围是____.例3已知方程(ln x)/x=x~2-2ex+a有实数解,则实数a的取值范围是____.在面对这类题时,很多考生往往会束手无策.考生如果能了解函数f(x)=(ln x)/x的性质,就可以使这类题迎刃而解了.
Candidates often encounter such a kind of functional property test questions when they practice and test: Example 1 It is known that the domain and range of the function f (x) = a ~ x (a> 1) are both [m, n] m x holds true for any real number x, the real number a is ____. Example 3 Known equation (ln x) / x = x ~ 2-2ex + a real solution, the real number a range of ____. In the face of such questions, many candidates tend to be at a loss what to do. The nature of the function f (x) = (ln x) / x makes it easy to solve these problems.