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.