Draw the graph of `f(X)=log_(e)(1-log_(e)x)`. Find the point of inflection

Answer

Point of inflection : x=1

Explanation

`f(x) = log_(e)(1-log_(e)x)`
f(X) is defined if `1- log_(e)xgt0`
or `log_(e)xlt1`
or `0ltxlte`
`therefore` domain is (0,e)
Also `f(X) =-(1)/(1-log_(e)x).(1)/(x)ltx`
`rarr` f(X) is continous and decreasing `forall` x in its domain
further `underset(xrarr0)lim log_(e)(1-l^(-))=log_(e)0^(+)=-oo`
For point of inflection `f(X)=(-log_(e)x)/(x^(2)(1-log_(e)x)^(2))`
clear f(1) =0 so x =1 which is a point of inflection graph is as shown in the following figure

Form the graph y =0 and y = are asymtotes