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Hannibal lecter

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Registered: 2016-02-11

Posts: 392

what is the solution for f(x) = exp(-x) ?

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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Jai Ganesh

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Registered: 2005-06-28

Posts: 46,154

Re: what is the solution for f(x) = exp(-x) ?

Hi,

Hope this graph helps:

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zetafunc

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Registered: 2014-05-21

Posts: 2,432

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Re: what is the solution for f(x) = exp(-x) ?

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

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.

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

Hannibal lecter

Member

Registered: 2016-02-11

Posts: 392

Re: what is the solution for f(x) = exp(-x) ?

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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Wisdom is a tree which grows in the heart and fruits on the tongue

iamaditya

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From: Planet Mars

Registered: 2016-11-15

Posts: 821

Re: what is the solution for f(x) = exp(-x) ?

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

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Registered: 2010-06-20

Posts: 10,134

Re: what is the solution for f(x) = exp(-x) ?

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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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
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zetafunc

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Registered: 2014-05-21

Posts: 2,432

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Re: what is the solution for f(x) = exp(-x) ?

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: