# Thread: how to factor a polynomial to the yth degree

1. ## 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!

2. ## 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.

3. ## Re: how to factor a polynomial to the yth degree

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.

4. ## Re: how to factor a polynomial to the yth degree

kingsolomonsgrave, where did you get this question from?

5. ## Re: how to factor a polynomial to the yth degree

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!

6. ## Re: how to factor a polynomial to the yth degree

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'

7. ## Re: how to factor a polynomial to the yth degree

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 $f^{-1}(4)=0$.

8. ## 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:

9. ## Re: how to factor a polynomial to the yth degree

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!