how to factor a polynomial to the yth degree

• August 28th 2012, 04:07 PM
kingsolomonsgrave
how to factor a polynomial to the yth degree
How would I go about finding the inverse of the function f(x)=3+x+e^x

?

I can rewrite the forumla interchanging the x and y variables to obtain

x = 3+y+e^y

but I'm not sure where to go from here.

thanks!
• August 28th 2012, 05:23 PM
MaxJasper
Re: how to factor a polynomial to the yth degree
1st you should find x in terms of y as x=g(y), then switch x & y positions and check domain and range values.
• August 28th 2012, 06:43 PM
Prove It
Re: how to factor a polynomial to the yth degree
Quote:

Originally Posted by kingsolomonsgrave
How would I go about finding the inverse of the function f(x)=3+x+e^x

?

I can rewrite the forumla interchanging the x and y variables to obtain

x = 3+y+e^y

but I'm not sure where to go from here.

thanks!

You will not be able to get an explicit equation y in terms of x, because of the fact that y is both "inside" a polynomial function and a transcendental function.
• August 28th 2012, 09:14 PM
Vlasev
Re: how to factor a polynomial to the yth degree
kingsolomonsgrave, where did you get this question from?
• August 29th 2012, 02:40 AM
kingsolomonsgrave
Re: how to factor a polynomial to the yth degree
Quote:

Originally Posted by Prove It
You will not be able to get an explicit equation y in terms of x, because of the fact that y is both "inside" a polynomial function and a transcendental function.

thanks!
• August 29th 2012, 02:45 AM
kingsolomonsgrave
Re: how to factor a polynomial to the yth degree
Quote:

Originally Posted by Vlasev
kingsolomonsgrave, where did you get this question from?

I got this from section 1.6 of James Stewart's 7th edition of Calculus

this one: http://www.amazon.com/Calculus-Trans.../dp/0538497904

the full question says

f(x)=3+x+e^x and then asks what f^-1(4) is

NOTE: by f^-1(4) I mean 'the inverse function of f at 4'
• August 29th 2012, 03:17 AM
Plato
Re: how to factor a polynomial to the yth degree
Quote:

Originally Posted by kingsolomonsgrave
the full question says
f(x)=3+x+e^x and then asks what f^-1(4) is

Looking at the derivative, it easy to see that function is one-to-one.
So $f(0)=4$ thus $f^{-1}(4)=0$.
• August 29th 2012, 09:13 AM
MaxJasper
Re: how to factor a polynomial to the yth degree
It appears that your own solution is the best mirror image on y=x line:

http://mathhelpforum.com/attachment....1&d=1346260719
• August 29th 2012, 09:58 AM
kingsolomonsgrave
Re: how to factor a polynomial to the yth degree
Quote:

Originally Posted by Plato
Looking at the derivative, it easy to see that function is one-to-one.
So $f(0)=4$ thus $f^{-1}(4)=0$.

Oh i see what the question was getting at now!