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Scorpion4ik [409]
3 years ago
15

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

Mathematics
1 answer:
Snezhnost [94]3 years ago
3 0
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.
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