i think it is A. P(5<X<9)
Instead of putting the diving put the multiply and you’re answer will be correct
As points, x-intercepts take the form
![(x,0)](https://tex.z-dn.net/?f=%28x%2C0%29)
, so to find the intercepts we can set
![y=0](https://tex.z-dn.net/?f=y%3D0)
and solve for
![x](https://tex.z-dn.net/?f=x)
.
![x\ln(x+e)=0\implies\begin{cases}x=0\\\ln(x+e)=0\end{cases}](https://tex.z-dn.net/?f=x%5Cln%28x%2Be%29%3D0%5Cimplies%5Cbegin%7Bcases%7Dx%3D0%5C%5C%5Cln%28x%2Be%29%3D0%5Cend%7Bcases%7D)
From the first equation alone, we already know that
![x=0](https://tex.z-dn.net/?f=x%3D0)
is a solution, which means one intercept is
![(0,0)](https://tex.z-dn.net/?f=%280%2C0%29)
.
The second equation gives
![\ln(x+e)=0\implies e^{\ln(x+e)}=e^0\implies x+e=1\implies x=1-e](https://tex.z-dn.net/?f=%5Cln%28x%2Be%29%3D0%5Cimplies%20e%5E%7B%5Cln%28x%2Be%29%7D%3De%5E0%5Cimplies%20x%2Be%3D1%5Cimplies%20x%3D1-e)
so that the second intercept occurs at
![(1-e,0)](https://tex.z-dn.net/?f=%281-e%2C0%29)
.
So if
![a=0](https://tex.z-dn.net/?f=a%3D0)
and
![b=1-e](https://tex.z-dn.net/?f=b%3D1-e)
, we have
![a+b=1-e](https://tex.z-dn.net/?f=a%2Bb%3D1-e)
, giving C as the answer.