# Thread: How to convert these functions

1. ## How to convert these functions

Hello there!

In my work, I will have to convert functions. My English is crap, so I will just show you what I mean.

If I have a function:

y = x + 1 i can convert it to look like this: x = y - 1. I would like to do the same for:

y = x^3 + x^2 + x + 1

or this:

y = x^4 + x^3 + x^2 + x + 1

or this:

y = x^5 + x^4 + x^3 + x^2 + x + 1

How is that done?

Thank you.

Kind regards,
Marius

2. For the first, you have this. For the second, you have this. For the third, in general, the quintic polynomial is not solvable (that's been proved, actually). Certain special cases can be solved, but not the general quintic.

3. Thank you!

y = x^2 + x + 1

Kind regards,
Marius

4. That one's a quadratic. Rewrite as

$\displaystyle x^{2}+x+1-y=0,$ and use the quadratic formula to solve:

$\displaystyle x=\dfrac{-1\pm\sqrt{1-4(1-y)}}{2}=\dfrac{-1\pm\sqrt{4y-3}}{2}.$

Note that in order for everything to be real, you'd need $\displaystyle 4y-3\ge 0,$ or $\displaystyle y\ge 3/4.$

5. Thanks for that!

I found this one for the cubic:

But couldnt find one for the quartic on wikipedia. Do you know what it looks like?

Thanks! M

6. Originally Posted by king.oslo
Hello there!

In my work, I will have to convert functions. My English is crap, so I will just show you what I mean.

If I have a function:

y = x + 1 i can convert it to look like this: x = y - 1. I would like to do the same for:

y = x^3 + x^2 + x + 1
This is a cubic.

or this:

y = x^4 + x^3 + x^2 + x + 1
This is a quartic.

or this:

y = x^5 + x^4 + x^3 + x^2 + x + 1
This is a quintic.

How is that done?

Thank you.

Kind regards,
Marius
I don't know where you found your "cubic" formula, but it's not nearly complicated enough for a cubic. It looks like an incorrect quadratic. Here's the solution for your cubic. Here's the solution for your quartic.

7. Originally Posted by Ackbeet
This is a cubic.

This is a quartic.

This is a quintic.

I don't know where you found your "cubic" formula, but it's not nearly complicated enough for a cubic. It looks like an incorrect quadratic. Here's the solution for your cubic. Here's the solution for your quartic.
Thanks! M

8. You're welcome!

9. A polynomial equation of degree 5 or higher cannot be solved in terms of radicals. There methods, using "special functions" for solving such equations.

10. Really? I didn't know that! Just doing a simple google search brought up the Jacobi theta function method, as well as hypergeometric functions (hypergeometric functions do seem to show up lots of different places, don't they? Maybe that's why the Russians do everything in terms of them.), as possibilities for solving the general quintic.