Triagle
contestada

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

Respuesta :

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

[tex]x\ln(x+e)=0\implies\begin{cases}x=0\\\ln(x+e)=0\end{cases}[/tex]

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

The second equation gives

[tex]\ln(x+e)=0\implies e^{\ln(x+e)}=e^0\implies x+e=1\implies x=1-e[/tex]

so that the second intercept occurs at [tex](1-e,0)[/tex].

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

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