SOLUTION: find the zeros of the function f(x)=xe^-x -e^-x

Set right side equal to zero:



Factor out 



Now we set each factor equal to zero.

Setting first factor = 0:



That part has no solution since a positive
number raise to any power is always positive
and thus can never equal to 0.

Setting  = 0





So 1 is the only solution.

Edwin