# Equation has exactly 2 solutions

• Jul 6th 2010, 02:39 AM
Utherr
Equation has exactly 2 solutions
$\displaystyle m(x+1)=e^{|x|}$

Find $\displaystyle m\in\mathbb{R}$ so that the equation has exactly two solutions. I really don't know where to start... but for that equation to have any solutions $\displaystyle m(x+1)$ has to be positive and non-zero.

One answer from below is corect:

$\displaystyle A) m\in(1,\infty)$
$\displaystyle B) m\in(-\infty,-e^2)\cup(1,\infty)$
$\displaystyle C) m\in(-\infty,-e^2]\cup[1,\infty)$
$\displaystyle D) m\in(-\infty,-e^2)\cup(0,1)$
$\displaystyle E) m\in{\O}$
F) none of the above
• Jul 6th 2010, 02:56 AM
pickslides
Quote:

Originally Posted by Utherr
$\displaystyle m(x+1)=e^{|x|}$

Well $\displaystyle m(x+1)$ is linear and this looks like $\displaystyle e^x$ for $\displaystyle x\in (0,\infty)$ and then reflected again in the y-axis giving a fat looking parabola.

Quote:

Originally Posted by Utherr
$\displaystyle m(x+1)=e^{|x|}$
but for that equation to have any solutions $\displaystyle m(x+1)$ has to be positive and non-zero.

do you mean $\displaystyle m$ has to be positive? If so think again, when $\displaystyle m=-9$ you have two solutions
• Jul 6th 2010, 06:59 AM
mr fantastic
Quote:

Originally Posted by Utherr
$\displaystyle m(x+1)=e^{|x|}$

Find $\displaystyle m\in\mathbb{R}$ so that the equation has exactly two solutions. I really don't know where to start... but for that equation to have any solutions $\displaystyle m(x+1)$ has to be positive and non-zero.

One answer from below is corect:

$\displaystyle A) m\in(1,\infty)$
$\displaystyle B) m\in(-\infty,-e^2)\cup(1,\infty)$
$\displaystyle C) m\in(-\infty,-e^2]\cup[1,\infty)$
$\displaystyle D) m\in(-\infty,-e^2)\cup(0,1)$
$\displaystyle E) m\in{\O}$
F) none of the above

Draw the graph of $\displaystyle y = e^{|x|}$. Now draw possible graphs of $\displaystyle y = m(x + 1)$, taking into account each given option. Come to a conclusion.