Question

The function y = x * ln(x + e) has two distinct x intercepts. One is at x = a and the other is at x = b. The value of a + b is

a) 0
b) undefined
c) 1 - e ***
d) 1
e) e - 1

Answer 1

As points, x-intercepts take the form $(x,0)$, so to find the intercepts we can set $y=0$ and solve for $x$.

$x\ln(x+e)=0\implies\begin{cases}x=0\\\ln(x+e)=0\end{cases}$

From the first equation alone, we already know that $x=0$ is a solution, which means one intercept is $(0,0)$.

The second equation gives

$\ln(x+e)=0\implies e^{\ln(x+e)}=e^0\implies x+e=1\implies x=1-e$

so that the second intercept occurs at $(1-e,0)$.

So if $a=0$ and $b=1-e$, we have $a+b=1-e$, giving C as the answer.