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**Hannibal lecter****Member**- Registered: 2016-02-11
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Hi, is there a root for the f(x) = e^-x ???

is it close to 0.571143115080177? or that wrong there is no any root?

please help me

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 23,578

Hi,

Hope this graph helps:

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Hannibal lecter wrote:

raised to the power of anything won't ever have a root, because the exponential function is always positive. You can see this in the graph that ganesh posted -- it won't ever touch (nor go below) the x-axis.Hi, is there a root for the f(x) = e^-x ???

is it close to 0.571143115080177? or that wrong there is no any root?

please help me

Where did you get 0.571143115080177 from? Are you stating the problem correctly? Or is something else meant by the word 'root' here?

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**Hannibal lecter****Member**- Registered: 2016-02-11
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I tried a matlab code to solve it, but thanks for helping I know it's nor have a root now..

but what about exp(-x)=x?

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**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
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zetafunc wrote:

Where did you get 0.571143115080177 from?

See the graph which Ganesh posted. You will see that it converges down to X-axis and almost touches it at that value.

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**bob bundy****Administrator**- Registered: 2010-06-20
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See here:

http://www.mathsisfun.com/data/function … nc1=e^(-x)

Just add y = x as the second function and you'll see it does have that value as the solution.

Bob

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iamaditya wrote:

See the graph which Ganesh posted. You will see that it converges down to X-axis and almost touches it at that value.

No, it doesn't ever touch the x-axis. The exponential function is strictly positive: it can't have any roots.

However, if we take , then there is indeed a root. In fact, if we allow complex solutions, there are infinitely many of them, and they are precisely the nth values of the Lambert-W function, . This sequence generates all the complex roots.There is one real root, the so-called Omega constant, . There are several exact forms for the Omega constant, such as the 'power tower':and a nice integral relation is:

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